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https://feeds.library.caltech.edu/people/Morari-M/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 07 Feb 2024 04:23:10 +0000Robust stability of systems with integral control
https://resolver.caltech.edu/CaltechAUTHORS:20170727-173834553
Authors: {'items': [{'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1983
DOI: 10.1109/CDC.1983.269645
A necessary and sufficient condition is derived which must be satisfied by the plant steady state gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is unconditionally stable. Based on this theorem the robustness of integral control systems is analyzed, i.e. the family of plants is defined which are stable when controlled with the same integral controller. Conditions for actuator/sensor failure tolerance of systems with integral control are also given. Finally, parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vymrz-5wf09Robust stability of systems with integral control
https://resolver.caltech.edu/CaltechAUTHORS:20170724-175321072
Authors: {'items': [{'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1985
DOI: 10.1109/TAC.1985.1104012
A number of necessary and sufficient conditions are derived, which must be satisfied by the plant d.c. gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable. Based on these results, the robustness of integral control systems is analyzed, i.e., the family of plants is defined which are stable when controlled with the same integral controller. Conditions for actuator/sensor failure tolerance of systems with integral control are also given. Finally, parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hap13-gf666Newton control laws for nonlinear controller design
https://resolver.caltech.edu/CaltechAUTHORS:20170719-172851214
Authors: {'items': [{'id': 'Economou-C-G', 'name': {'family': 'Economou', 'given': 'Constantin G.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1985
DOI: 10.1109/CDC.1985.268732
Strong similarities between control theory and the theory on the solution of operator equations have been observed and basic results in control theory have been derived from operator theory arguments. The purpose of this work is to use the underlying duality in order to develop analysis and synthesis techniques for nonlinear systems. As an example, controllers induced by the Newton method are introduced and the corresponding stability characteristics are studied. The concepts are demonstrated by applications to linear and nonlinear systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/58wrn-4qn41Waveform relaxation for concurrent dynamic simulation of distillation columns
https://resolver.caltech.edu/CaltechAUTHORS:20161219-164724261
Authors: {'items': [{'id': 'Skjellum-A', 'name': {'family': 'Skjellum', 'given': 'Anthony'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Mattisson-S', 'name': {'family': 'Mattisson', 'given': 'Sven'}}]}
Year: 1988
DOI: 10.1145/63047.63060
he need for cost-effective, high-speed computing is essential in many aspects of chemical engineering practice, notably for the simulation of large-scale dynamic systems. The arrival of powerful, highly concurrent message-passing multicomputers potentially offers such economical large-scale computing capability [13,14]. Development of appropriate, efficient algorithms which realize this potential must therefore become an important area of ongoing research and development in chemical engineering. Desired orders-of-magnitude speedup strongly motivates the use of novel algorithmic approaches for large-scale simulation.
Initially, we are developing a simplified binary distillation simulation using the waveform relaxation paradigm [1-7]. Waveform relaxation has proven successful for the concurrent simulation of large-scale VLSI circuits [1-3,6,7] and is therefore a promising approach. Rather than an end in itself, however, we expect that results of this research effort will prove relevant to more general concurrent dynamic simulation including rigorous multicomponent distillation and chemical process flowsheeting. We describe the implementation effort (which generalizes the pre-existing CONCISEVLSI circuit simulator, [6]), the simplified distillation model, design issues and current status including a sketch of the underlying waveform relaxation algorithm and its realization. Elsewhere we report further observations as well as speedup results [15].https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6erjx-8nd49Robust control of ill-conditioned plants: high-purity distillation
https://resolver.caltech.edu/CaltechAUTHORS:SKOieeetac88
Authors: {'items': [{'id': 'Skogestad-S', 'name': {'family': 'Skogestad', 'given': 'Sigurd'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}]}
Year: 1988
DOI: 10.1109/9.14431
Using a high-purity distillation column as an example, the physical reason for the poor conditioning and its implications on control system design and performance are explained. It is shown that an acceptable performance/robustness tradeoff cannot be obtained by simple loop-shaping techniques (using singular values) and that a good understanding of the model uncertainty is essential for robust control system design. Physically motivated uncertainty descriptions (actuator uncertainties) are translated into the H∞/structured singular value framework, which is demonstrated to be a powerful tool to analyze and understand the complex phenomena.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zsw7h-hdy73Robust Controller Design for a Nonlinear CSTR
https://resolver.caltech.edu/CaltechAUTHORS:20170710-173942278
Authors: {'items': [{'id': 'Doyle-F-J-III', 'name': {'family': 'Doyle', 'given': 'Francis J., III'}}, {'id': 'Packard-A-K', 'name': {'family': 'Packard', 'given': 'Andrew K.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1989
A design methodology is presented for the analysis and synthesis of robust linear controllers for a nonlinear continuous stirred tank reactor. Regions are defined in the phase plane in which the maintenance of robust stability and the achievement of robust performance levels are guaranteed. The results are based upon new extensions of the structured singular value theory to a class of nonlinear and time-varying systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rv68q-wf941Multivariable Anti-Windup and Bumpless Transfer: A General Theory
https://resolver.caltech.edu/CaltechAUTHORS:20170711-150034581
Authors: {'items': [{'id': 'Campo-P-J', 'name': {'family': 'Campo', 'given': 'P. J.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}, {'id': 'Nett-C-N', 'name': {'family': 'Nett', 'given': 'C. N.'}}]}
Year: 1989
A general theory is developed to address the anti-windup/bumpless transfer (AWBT) problem. Analysis results applicable to any linear time invariant system subject to plant input limitations and substitutions are presented. Quantitative performance objectives for AWBT compensation are outlined and several proposed AWBT methods are evaluated in light of these objectives. A synthesis procedure which highlights the performance trade-offs for AWBT compensation design is outlined.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vev8t-ave69Concurrent DASSL Applied to Dynamic Distillation Column Simulation
https://resolver.caltech.edu/CaltechAUTHORS:20170626-171949369
Authors: {'items': [{'id': 'Skjellum-A', 'name': {'family': 'Skjellum', 'given': 'Anthony'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1990
DOI: 10.1109/DMCC.1990.555439
The accurate, high-speed solution of systems of ordinary differential-algebraic equations (DAE's) of low index is of great importance in chemical, electrical and other engineering disciplines. Petzold's Fortran-based DASSL is the most widely used sequential code for solving DAE's. We have devised and implemented a completely new C code, Concurrent DASSL, specifically for multicomputers and patterned on DASSL. In this work, we address the issues of data distribution and the performance of the overall algorithm, rather than just that of individual steps. Concurrent DASSL is designed as an open, application-independent environment below which linear algebra algorithms may be added in addition to standard support for dense and sparse algorithms. The user may furthermore attach explicit data interconversions between the main computational steps, or choose compromise distributions. A "problem formulator" (simulation layer) must be constructed above Concurrent DASSL, for any specific problem domain. We indicate performance for a particular chemical engineering application, a sequence of coupled distillation columns. Future efforts are cited in conclusion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g1avm-gn647Robust Inferential Control for a Packed-Bed Reactor
https://resolver.caltech.edu/CaltechAUTHORS:20170627-173246670
Authors: {'items': [{'id': 'Budman-H-M', 'name': {'family': 'Budman', 'given': 'Hector M.'}}, {'id': 'Webb-C', 'name': {'family': 'Webb', 'given': 'Christopher'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1990
An inferential robust control technique is applied to an experimental fixed bed reactor. The controlled variables are the exit concentration and the maximum bed temperature. Both controlled variables are inferred from one single temperature measurement. The location of this measurement is selected to optimize the performance of the closed-loop system when model uncertainty is allowed. Closed-loop experiments are conducted to test the robustness characteristics of the controller. From these experiments, the operating regions most sensitive to modelling uncertainty are determined. The nonlinear system characteristics can cause significant offset in the inferred controlled variables.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tktky-cdt52A Conic Sector-Based Methodology for Nonlinear Control Design
https://resolver.caltech.edu/CaltechAUTHORS:20170627-170608548
Authors: {'items': [{'id': 'Doyle-F-J-III', 'name': {'family': 'Doyle', 'given': 'Francis J., III'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1990
A design method is presented for the analysis and synthesis of robust nonlinear controllers for chemical engineering systems. The method rigorously treats the effect of unmeasured disturbances and unmodeled dynamics on the stability and performance properties of a nonlinear system. The results utilise new extensions of structured singular value theory for analysis and recent synthesis results for approximate linearisation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6xcvw-02y84Integral controllability of integrating systems
https://resolver.caltech.edu/CaltechAUTHORS:20180315-134451137
Authors: {'items': [{'id': 'Grosdidier-P', 'name': {'family': 'Grosdidier', 'given': 'Pierre'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1990
DOI: 10.1021/ie00106a031
Necessary and sufficient conditions are derived for the integral controllability of single-input, single-output systems with an integrator.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wngcp-rh893Inadequacy of steady-state analysis for feedback control: distillate-bottom control of distillation columns
https://resolver.caltech.edu/CaltechAUTHORS:20180521-104147214
Authors: {'items': [{'id': 'Skogestad-S', 'name': {'family': 'Skogestad', 'given': 'Sigurd'}}, {'id': 'Jacobsen-E-W', 'name': {'family': 'Jacobsen', 'given': 'Elling W.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1990
DOI: 10.1021/ie00108a006
It is often claimed that for distillation columns the steady-state description is much more important than the dynamic description for control purposes. The ultimate counterexample to this misconception is the recently proposed distillate-bottom (DB) configuration that involves using distillate and bottom flow to control compositions. This control scheme has previously been labeled
"impossible" by most distillation control experts because D and B are not independent at steady state (since D + B = F) and the gain matrix is singular. Yet, as shown by Finco et al. for a propane-propylene splitter, both with simulations and with implementation, the scheme does actually
work. Finco et al. do not provide any explanations for this, but as shown in this paper, the main reason is the flow dynamics (liquid lag from the top to the bottom of the column), which decouples the responses at high frequency (initial response) and makes the system quite easy to control. The results in this paper demonstrate that steady-state data may be entirely misleading for evaluating
control performance. This is of course well-known, for example, from the Ziegler-Nichols tuning rules, which are based on high-frequency behavior only, but often seems to be forgotten when analyzing multivariable systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wmsza-vn350DAWRS: A Differential - Algebraic System Solver by the Waveform Relaxation Method
https://resolver.caltech.edu/CaltechAUTHORS:20170619-161314349
Authors: {'items': [{'id': 'Secchi-A-R', 'name': {'family': 'Secchi', 'given': 'Argimiro R.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Biscaia-E-C-Jr', 'name': {'family': 'Biscaia', 'given': 'Evaristo C., Jr.'}}]}
Year: 1991
DOI: 10.1109/DMCC.1991.633306
We investigate the concurrent solution of low-index
differential-algebraic equations (DAE's) by the waveform
relaxation (WR) method, an iterative method for system
integration. We present our new simulation code, DAWRS
(Differential - Algebraic - Waveform Relaxation Solver), to
solve DAE's on parallel machines using the WR methods, and
describe new techniques to improve the convergence of
such methods. As experimental results, we demonstrate the achievable concurrent performance to solve DAE's for
a class of applications in chemical engineering.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t6mx6-q5e13μ-sensitivities as an aid for robust identification
https://resolver.caltech.edu/CaltechAUTHORS:20170620-161438264
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'R. D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}]}
Year: 1991
Identification for a model for robust control design is more complicated than for the standard linear system transfer function model-the structure of the uncertainty as well as bounds on its size must be determined. It is especially unclear as to which parts of the system should be better modeled to improve robust performance. This paper addresses this question through some new tools, the μ-sensitivities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g3hwd-54d75PLS-Based Robust Inferential Control for a Packed-Bed Reactor
https://resolver.caltech.edu/CaltechAUTHORS:20170619-172208220
Authors: {'items': [{'id': 'Budman-H-M', 'name': {'family': 'Budman', 'given': 'H. M.'}}, {'id': 'Holcomb-T', 'name': {'family': 'Holcomb', 'given': 'T.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}]}
Year: 1991
This paper compares the performance of two different inferential schemes when applied to an experimental packed-bed reactor. The first scheme, proposed initially by Brosilow, is designed based on Kalman filter estimation. The second less traditional design uses an estimator computed from the Partial Least Squares regression method (PLS). The second approach was found to give superior performance when the nonlinear system under study is operated is a wide range of operating points. Due to the nonlinearity of the system it is essential to address the issue of robustness of the proposed schemes. This is formally done in this work using Structured Singular Value Theory. For the robustness analysis it is crucial to develop a realistic but not overly conservative uncertainty description. Since the PLS estimator uses a large number of measurements, a robust design based on the uncertainty associated with each one of the measurements would be very conservative. To overcome this problem a lumped uncertainty description is proposed which is identified directly from experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qmgqb-ate39Local Training for Radial Basis Function Networks: Towards Solving the Hidden Unit Problem
https://resolver.caltech.edu/CaltechAUTHORS:20170626-153041273
Authors: {'items': [{'id': 'Holcomb-T', 'name': {'family': 'Holcomb', 'given': 'Tyler'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1991
This work examines training methods for radial basis function networks (RBFNs). First, the theoretical and practical motivation for RBFNs is reviewed, as are two currently popular training methods. Next a new training method is developed using well known results from functional analysis. This method trains each kidden unit individually, and is thus called the local training method. The structure of the method allows analysis of individual hidden units; moreover a covariance-related quantity is defined that gives insight into how many hidden units to employ. Two examples illustrate the usefulness of the method. Lastly, an ad hoc method to further improve RBFN performance is demonstrated.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h5vya-fxg11Dynamics of homogeneous azeotropic distillation columns
https://resolver.caltech.edu/CaltechAUTHORS:20180524-154943435
Authors: {'items': [{'id': 'Andersen-H-W', 'name': {'family': 'Andersen', 'given': 'Henrik W.'}}, {'id': 'Laroche-L', 'name': {'family': 'Laroche', 'given': 'Lionel'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1991
DOI: 10.1021/ie00056a026
The dynamics of azeotropic distillation columns are significantly more complicated than those of simple binary columns. For changes in the internal flows, we initially observe a response in overall separation with a time constant that is similar to the one observed in binary distillation. However, we also observe a slow time-constant response, which is due to changes in the relative amount of entrainer in the extractive section. The fact that the gains for these two effects have different signs causes overshoot and, depending on the operating point, may also cause inverse responses with significant time constants. None of these phenomena are observed in binary distillation. They can be modeled by a simple second-order model. We also examine the open-loop dynamics for configurations aimed at dual-composition control. Just as in binary distillation there is a "high gain direction" that is obtained for changes in the external flows. The dynamics of this direction are hardly affected by changes in the operating point. The "low gain direction" is obtained for changes in the internal flows, just as in binary distillation, and also for changes in the entrainer feed flow rate. The properties of this direction change significantly with the operating point. For some operating points we observe overshoot and for others multivariable right-half-plane transmission zeros not observed in binary distillation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kq5ve-w3811Comments on "Tuning controllers on distillation columns with the distillate-bottoms structure"
https://resolver.caltech.edu/CaltechAUTHORS:20180514-154350854
Authors: {'items': [{'id': 'Skogestad-S', 'name': {'family': 'Skogestad', 'given': 'Sigurd'}}, {'id': 'Jacobsen-E-W', 'name': {'family': 'Jacobsen', 'given': 'Elling W.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1991
DOI: 10.1021/ie00056a056
Sir: A recent paper by Papastathopoulou and Luyben
(1990) discusses modeling and controller tuning of distillation columns using the DB scheme. We would like to
point out that their main result, which is to show how
models for the DB scheme may be derived from more
conventional control structures provided the liquid flow
dynamics are included, is taken from the work of Skogestad
and co-workers (1989a,b, 1990a,b). There are also two misconceptions in their paper that deserve comments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/42xpj-69s35Avery Final Report: Identification and Cross-Directional Control of Coating Processes
https://resolver.caltech.edu/CaltechCDSTR:1992.004
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Tyler-M-L', 'name': {'family': 'Tyler', 'given': 'Matthew L.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1992
Coating refers to the covering of a solid with a uniform layer of liquid. Of special industrial interest is the cross-directional control of coating processes, where the cross-direction refers to the direction perpendicular to the substrate movement. The objective of the controller is to maintain a uniform coating under unmeasured process disturbances.
Assumptions that are relevant to coating processes found in industry are used to develop a model for control design. We show how to identify the model from input-output data. This model is used to derive a model predictive controller to maintain flat profiles of coating across the substrate by varying the liquid flows along the cross direction.
The model predictive controller computes the control action which minimizes the predicted deviation in cross-directional uniformity. The predictor combines the estimate obtained from the model with the measurement of the cross-directional uniformity to obtain a prediction for the next time step. A filter is used to obtain robustness to model error and insensitivity to measurement noise. The tuning of the noise filter and different methods for handling actuator constraints are studied in detail. The three different constraint-handling methods studied are: the weighting of actuator movements in the objective function, explicitly adding constraints to the control algorithm, i.e. constrained model predictive control, and scaling infeasible control actions calculated from an unconstrained control law to be feasible.
Actuator constraints, measurement noise, model uncertainty, and the plant condition number are investigated to determine which of these limit the achievable closed loop performance. From knowledge of how these limitations affect the performance we find how the plant could be modified to improve the process uniformity. Also, because identification of model parameters is time-consuming and costly, we study how accurate the identification must be to achieve a given level of performance.
The theory developed throughout the paper is rigorously verified though simulations and experiments on a pilot plant. The effect of interactions on the closed loop performance is shown to be negligible for this pilot plant. The measurement noise and the actuator constraints are shown to have the largest effect on closed loop performance.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/94qmz-vz212Robust Control for a Noncolocated Spring-Mass System
https://resolver.caltech.edu/CaltechAUTHORS:20170613-173733581
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1992
Robust control laws are presented for an undamped pair of coupled manes with a noncolocated sensor and actuator. This simple problem captures many of the features of more complex aircraft and space structure vibration control problems. The control problem is formulated in the structured singular value framework, which addresses the stability robustness to parameter variations directly. Controllers are designed by D-K iteration (commonly called μ-synthesis), and the resulting high-order controllers are reduced using Hankel model reduction. Design specifications such as settling time, actuator constraints insensitivity to measurement noise, and parameter uncertainty are achieved by the resulting controllers. Design Problems #1 and #2 were considered in [2]. Design Problem #4 in [11] will be considered in this paper.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w10fj-kcd72On Nonlinear Systems with Poorly Behaved Zero Dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20170606-164219983
Authors: {'items': [{'id': 'Doyle-F-III', 'name': {'family': 'Doyle', 'given': 'F., III'}}, {'id': 'Allgöwer-F', 'name': {'family': 'Allgöwer', 'given': 'F.'}}, {'id': 'Oliveira-S', 'name': {'family': 'Oliveira', 'given': 'S.'}}, {'id': 'Gilles-E', 'name': {'family': 'Gilles', 'given': 'E.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}]}
Year: 1992
The design of controllers for nonlinear, nonminimum-phase systems is very challenging and is currently considered to be one of the most difficult theoretical control problems. Most control algorithms for nonlinear processes perform a linearization making use of an inverse of the system. In the linear case, the system can be factored into the minimum-phase and the nonminimum-phase parts and only the first one is inverted for purpose of control design. A similar scheme for nonlinear systems is still under investigation.
The present work adresses the problem of synthesizing nonlinear state feedback controllers for nonlinear, nonminimum-phase processes in three different ways. The first approach consists of a partial linearization which preserves stability by using an approximate stable/anti-stable factorization. The second technique can be viewed as an inner-outer factorization based approach. And, finally, in the single-output case, it is shown (through an example) that stabilization of the internal dynamics of a nonmininum-phase system can be achieved by using an additional input if this is feasible in practice. In this case, the manipulated variables have different roles, i.e., one is chosen such as to input/output feedback linearize the system and the second is used to locally stabilize the resulting nonminimum-phase internal dynamics.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/acpn5-fqq86Identification and Cross-Directional Control of Coating Processes: Theory and Experiments
https://resolver.caltech.edu/CaltechAUTHORS:20170613-172633659
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Tyler-M-L', 'name': {'family': 'Tyler', 'given': 'Matthew L.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Pranckh-F-R', 'name': {'family': 'Pranckh', 'given': 'Ferdinand R.'}}, {'id': 'Sartor-L', 'name': {'family': 'Sartor', 'given': 'Luigi'}}]}
Year: 1992
Of special industrial interest is the cross-directional control of continuous coating processes, where the cross-direction refers to the direction perpendicular to the substrate movement. The objective of the controller is to maintain a uniform coating under unmeasured process disturbances based on assumptions relevant to coating processes found in industry. A model for control design is developed. This model is used to derive a model predictive controller with the objective of maintaining flat profiles of coating across the substrate by varying the liquid flows along the cross direction. Actuator constraints, measurement noise, and model uncertainty are investigated to determine which of these limit the achivable closed loop performance. From a knowledge of the effect of these limitations on performance we determine how the plant could be modified to improve the coating uniformity. The theory developed throughout the paper is rigorously verified though experiments on an industrial pilot plant.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/djmrf-r3693Robust Inferential Control for a Packed-Bed Reactor
https://resolver.caltech.edu/CaltechAUTHORS:20180524-162132927
Authors: {'items': [{'id': 'Budman-H-M', 'name': {'family': 'Budman', 'given': 'Hector M.'}}, {'id': 'Webb-C-J', 'name': {'family': 'Webb', 'given': 'Chris'}}, {'id': 'Holcomb-T-R', 'name': {'family': 'Holcomb', 'given': 'Tyler R.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1992
DOI: 10.1021/ie00007a013
Two different inferential control schemes are applied to an experimental fixed bed methanation reactor. The first scheme, proposed initially by Brosilow, is designed based on Kalman filter estimation. The second less traditional design uses an estimator computed from the partial least squares regression method (PLS). The second approach was found to give superior performance when the nonlinear system under study is operated in a wide range of operating points. Due to the nonlinearity of the system it is essential to address the issue of robustness of the proposed schemes. This is formally done in this work using structured singular value theory. For the robustness analysis it is crucial to develop a realistic but not overly conservative uncertainty description. Since the PLS estimator uses a large number of measurements, a robust design based on the uncertainty associated with each one of the measurements would be very conservative. To overcome this problem, a lumped uncertainty description is proposed which is identified directly from experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wfs9t-6mr02Comparison of internal model control and linear quadratic optimal control for SISO systems
https://resolver.caltech.edu/CaltechAUTHORS:20180524-160947847
Authors: {'items': [{'id': 'Scali-C', 'name': {'family': 'Scali', 'given': 'Claudio'}}, {'id': 'Semino-D', 'name': {'family': 'Semino', 'given': 'Daniele'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1992
DOI: 10.1021/ie00008a013
In this paper internal model control (IMC) is formulated for general inputs and compared with linear quadratic (H_2) optimal control (LQOC) with a general (dynamic) input penalty weight. Analogies and differences between the two methods for robustness study are clearly pointed out. Both controllers can be expressed in terms of the same nominal controller and a robustness filter. The main difference is that the LQOC filter depends also on process and disturbance parameters. As a consequence, performance may be different in general, even if in many cases quite similar results are obtained. The design for robustness is much more straightforward in IMC.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bjzxm-m4f22Homogeneous azeotropic distillation: separability and flowsheet synthesis
https://resolver.caltech.edu/CaltechAUTHORS:20180515-140536975
Authors: {'items': [{'id': 'Laroche-L', 'name': {'family': 'Laroche', 'given': 'Lionel'}}, {'id': 'Bekiaris-N', 'name': {'family': 'Bekiaris', 'given': 'Nikolaos'}}, {'id': 'Andersen-H-W', 'name': {'family': 'Andersen', 'given': 'Henrik W.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1992
DOI: 10.1021/ie00009a017
When designing a homogeneous azeotropic sequence which separates a binary azeotrope into two pure products, we must first choose the entrainer. In the case of homogeneous azeotropic distillation, separability at finite reflux and at infinite reflux are not equivalent and must be examined separately. By analyzing the profiles of columns operated at infinite reflux in detail, we have shown that a binary
azeotrope can be separated with only one distillation column. We present a necessary and sufficient condition which identifies such situations. We have found a necessary and sufficient condition for separability in a two-column sequence. When separation is feasible, this condition indicates the flowsheet of the corresponding separation sequence. We have also shown that separation is always feasible in a three-column separation if the azeotrope we want to separate is a saddle. Finally, we examine two situations where separation is feasible at finite reflux but not at infinite reflux.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cdnt5-7vz69State-Space Interpretation of Model Predictive Control
https://resolver.caltech.edu/CaltechCDSTR:1992.003
Authors: {'items': [{'id': 'Lee-J-H', 'name': {'family': 'Lee', 'given': 'Jay H.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Garcia-C-E', 'name': {'family': 'Garcia', 'given': 'Carlos E.'}}]}
Year: 1992
A model predictive control technique based on a step response model is developed using state estimation techniques. The standard step response model is extended so that integrating systems can be treated within the same framework. Based on the modified step response model, it is shown how the state estimation techniques from stochastic optimal control can be used to construct the optimal prediction vector without introducing significant additional numerical complexity. In the case of integrated or double integrated white noise disturbances filtered through general first-order dynamics and white measurement noise, the optimal filter gain is parametrized explicitly in terms of a single parameter between 0 and 1, thus removing the requirement for solving a Riccati equation and equipping the control system with useful on-line tuning parameters. Parallels are drawn to the existing MPC techniques such as Dynamic Matrix Control (DMC), Internal Model Control (IMC) and Generalized Predictive Control (GPC).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cpzwk-0tt39Multiple Steady States in Homogeneous Azeotropic Distillation
https://resolver.caltech.edu/CaltechCDSTR:1993.001
Authors: {'items': [{'id': 'Bekiaris-N', 'name': {'family': 'Bekiaris', 'given': 'Nikolaos'}}, {'id': 'Meski-G-A', 'name': {'family': 'Meski', 'given': 'George A.'}}, {'id': 'Radu-C-M', 'name': {'family': 'Radu', 'given': 'Christian M.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
In this article we study multiple steady states in ternary homogeneous azeotropic distillation. We show that in the case of infinite reflux and an infinite number of trays one can construct bifurcation diagrams on physical grounds with the distillate flow as the bifurcation parameter. Multiple steady states exist when the distillate flow varies non-monotonically along the continuation path of the bifurcation diagram. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the distillation region boundaries. We also locate in the composition triangle the feed compositions that lead to these multiple steady states. We further note that most of these results are independent of the thermodynamic model used. We show that the prediction of the existence of multiple steady states in the case of infinite reflux and an infinite number of trays has relevant implications for columns operating at finite reflux and with a finite number of trays. Using numerically constructed bifurcation diagrams for specific examples, we show that these multiplicities tend to vanish for small columns and/or for low reflux flows. Finally, we comment on the effect of multiplicities on column design and operation for some specific examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ebyd2-cth78Significance Regression: Improved Estimation from Collinear Data for the Measurement Error Model
https://resolver.caltech.edu/CaltechCDSTR:1993.004
Authors: {'items': [{'id': 'Holcomb-T-R', 'name': {'family': 'Holcomb', 'given': 'Tyler R.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
This paper examines improved regression methods for the linear multivariable measurement error model (MEM) when the data suffers from "collinearity." The difficulty collinearity presents for reliable estinlation is discussed and a systematic procedure, significance regression (SR-MEM), is developed to address collinearity. In addition to mitigating collinearity difficulties SR-MEM produces asymptotically unbiased estimates. The use of ordinary least squares (OLS) for the MEM is examined. For collinear data OLS can improve the mean squared error of estimation over the maximum likelihood (ML) unbiased estimator in a manner analogous to ridge regression (RR). The significance regression method developed for the classical model (SR-classical) can also be used for data with measurement errors. SR-classical is similar SR-MEM and can yield better estimation than the ML estimator for collinear data. Numerical examples illustrate several points.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ss8hw-crw26PLS Leads to Different Algorithms for Factor Analysis and Regression
https://resolver.caltech.edu/CaltechCDSTR:1993.003
Authors: {'items': [{'id': 'Holcomb-T', 'name': {'family': 'Holcomb', 'given': 'Tyler'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
Two multivariable problems of general interest, are factor analysis and regression. This paper examines partial least squares (PLS) as a tool for both problems. For single output data sets, the familiar PLS algorithm is applicable to both problems. For multiple output problems the familiar PLS algorithm [1, 2, 3] (called fact-PLS in this paper) is appropriate for factor analysis. However fact-PLS leads to algebraically-inconistent results for regression problems. To address this issue, a new algebraically-consistent multivariable PLS algorithm, C-PLS, is developed. Unlike fact-PLS, C-PLS does not rely on iterative calculations. Another PLS approach, "one-at-a-time" PLS (OAT-PLS), is closely related to C-PLS; however OAT-PLS is also algebraically-inconsistent. A simulation study of these various PLS methods shows C-PLS to have the best estimation and prediction performance.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jy0xn-xsh12Computational Complexity of μ Calculation
https://resolver.caltech.edu/CaltechCDSTR:1993.005
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Young-P-M', 'name': {'family': 'Young', 'given': 'Peter M.'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
The structured singular value μ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yy8es-83493Significance Regression: Robust Regression for Collinear Data
https://resolver.caltech.edu/CaltechCDSTR:1993.006
Authors: {'items': [{'id': 'Holcomb-T-R', 'name': {'family': 'Holcomb', 'given': 'Tyler R.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
This paper examines robust linear multivariable regression from collinear data. A brief review of M-estimators discusses the strengths of this approach for tolerating outliers and/or perturbations in the error distributions. The review reveals that M-estimation may be unreliable if the data exhibit collinearity. Next, significance regression (SR) is discussed. SR is a successful method for treating collinearity but is not robust. A new significance regression algorithm for the weighted-least-squares error criterion (SR-WLS) is developed. Using the weights computed via M-estimation with the SR-WLS algorithm yields an effective method that robustly mollifies collinearity problems. Numerical examples illustrate the main points.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bhg7f-gd956Significance Regression: A Statistical Approach to Biased Linear Regression and Partial Least Squares
https://resolver.caltech.edu/CaltechCDSTR:1993.002
Authors: {'items': [{'id': 'Holcomb-T-R', 'name': {'family': 'Holcomb', 'given': 'Tyler R.'}}, {'id': 'Hjalmarsson-H', 'name': {'family': 'Hjalmarsson', 'given': 'Hakan'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
This paper first examines the properties of biased regressors that proceed by restricting the search for the optimal regressor to a subspace. These properties suggest features such biased regression methods should incorporate. Motivated by these observations, this work proposes a new formulation for biased regression derived from the principle of statistical significance. This new formulation, significance regression (SR), leads to partial least squares (PLS) under certain model assumptions and to more general methods under various other model kumptions. For models with multiple outputs, SR will be shown to have certain advantages over PLS. Using the new formulation a significance test is advanced for determining the number of directions to be used; for PLS, cross-validation has been the primary method for determining this quantity. The prediction and estimation properties of SR are discussed. A brief numerical example illustrates the relationship between SR and PLS.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qd3jz-ds118Anti-Windup Design for Internal Model Control
https://resolver.caltech.edu/CaltechCDSTR:1993.007
Authors: {'items': [{'id': 'Zheng-A', 'name': {'family': 'Zheng', 'given': 'Alex'}}, {'id': 'Kothare-M-V', 'name': {'family': 'Kothare', 'given': 'Mayuresh V.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
This paper considers linear control design for systems with input magnitude saturation. A general anti-windup scheme which optimizes nonlinear performance, applicable to MIMO systems, is developed. Several examples, including an ill-conditioned plant, show that the scheme provides graceful degradation of performance. The attractive features of this scheme are its simplicity and effectiveness.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xjaqs-7mw41Robust Stability of Constrained Model Predictive Control
https://resolver.caltech.edu/CaltechAUTHORS:20120717-132756194
Authors: {'items': [{'id': 'Zheng-Zhi-Q', 'name': {'family': 'Zheng', 'given': 'Zhi Q.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
A new design technique for a robust model predictive controller is proposed using an uncertainty description expressed in the time-domain. Robust stability of the resulting closed-loop system is guaranteed for a set of Finite Impulse Response (FIR) models. Both necessary and sufficient conditions for asymptotic stability are stated. If the uncertainty is described as lower and upper bounds on impulse response coefficients, then the resulting optimization problem can be cast as a linear program of moderate size.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xdsek-jb697Multiple Steady States in Homogeneous Azeotropic Distillation
https://resolver.caltech.edu/CaltechAUTHORS:20170605-171718125
Authors: {'items': [{'id': 'Bekiaris-N', 'name': {'family': 'Bekiaris', 'given': 'Nikolaos'}}, {'id': 'Meski-G-A', 'name': {'family': 'Meski', 'given': 'George A.'}}, {'id': 'Radu-C-M', 'name': {'family': 'Radu', 'given': 'Christian M.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
In this article we study multiple steady states in ternary homogeneous azeotropic distillation. We show that in the case of infinite reflux and an infinite number of trays, multiple steady states exist when the distillate flow varies non-monotonically along the continuation path of the bifurcation diagram with the distillate flow as the bifurcation parameter. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the distillation region boundaries. We also locate in the composition triangle the feed compositions that lead to these multiple steady states. We show that the prediction of the existence of multiple steady states in the case of infinite reflux and an infinite number of trays has relevant implications for columns operating at finite reflux and with a finite number of trays. Using numerically constructed bifurcation diagrams for specific examples, we show that these multiplicities tend to vanish for small columns and/or for low reflux flows.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/am9zz-1fy60Computational complexity of μ calculation
https://resolver.caltech.edu/CaltechAUTHORS:20190320-132001216
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Young-P-M', 'name': {'family': 'Young', 'given': 'Peter M.'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
DOI: 10.23919/ACC.1993.4793162
The structured singular value μ measures the robustness of uncertain Systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r3w7x-hye17Stability and Performance Analysis of Systems Under Constraints
https://resolver.caltech.edu/CaltechCDSTR:1993.009
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
All real world control systems must deal with actuator and state constraints. Standard conic sector bounded nonlinearity stability theory provides methods for analyzing the stability and performance of systems under constraints, but it is well-known that these conditions can be very conservative. A method is developed to reduce conservatism in the analysis of constraints by representing them as nonlinear real parametric uncertainty.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2zdma-ddb77A Unified Framework for the Study of Anti-Windup Designs
https://resolver.caltech.edu/CaltechCDSTR:1993.011
Authors: {'items': [{'id': 'Kothare-M-V', 'name': {'family': 'Kothare', 'given': 'Mayuresh V.'}}, {'id': 'Campo-P-J', 'name': {'family': 'Campo', 'given': 'Peter J.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Nett-C-N', 'name': {'family': 'Nett', 'given': 'Carl N.'}}]}
Year: 1993
We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: "Design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance". The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. It is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model. The actual analysis of stability and performance, and robustness issues are problems in their own right and hence not detailed here. The main result is the unification of existing schemes for AWBT compensation under a general framework.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q4q91-jmt39Robust Control Structure Selection
https://resolver.caltech.edu/CaltechCDSTR:1993.012
Authors: {'items': [{'id': 'Lee-J-H', 'name': {'family': 'Lee', 'given': 'Jay H.'}}, {'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Packard-A', 'name': {'family': 'Packard', 'given': 'Andrew'}}]}
Year: 1993
Screening tools for control structure selection in the presence of model/plant mismatch are developed in the context of the Structured Singular Value (μ) theory. The developed screening tools are designed to aid engineers in the elimination of undesirable control structure candidates for which a robustly performing controller does not exist. Through application on a multicomponent distillation column, it is demonstrated that the developed screening tools can be effective in choosing an appropriate control structure while previously existing methods such as the Condition Number Criterion can lead to erroneous results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8qa3g-ndw41Multiple steady states in homogeneous azeotropic distillation
https://resolver.caltech.edu/CaltechAUTHORS:20180313-095039605
Authors: {'items': [{'id': 'Bekiaris-N', 'name': {'family': 'Bekiaris', 'given': 'Nikolaos'}}, {'id': 'Meski-G-A', 'name': {'family': 'Meski', 'given': 'George A.'}}, {'id': 'Radu-C-M', 'name': {'family': 'Radu', 'given': 'Cristian M.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
DOI: 10.1021/ie00021a026
In this article we study multiple steady states in ternary homogeneous azeotropic distillation. We show that in the case of infinite reflux and an infinite number of trays one can construct bifurcation diagrams on physical grounds with the distillate flow as the bifurcation parameter. Multiple steady
states exist when the distillate flow varies nonmonotonically along the continuation path of the bifurcation diagram. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the distillation region boundaries. We also locate in the composition triangle the feed compositions that lead to these multiple steady states. We further note that most of these results are independent of the thermodynamic model used. We show that the prediction of the existence of multiple steady states in the case of infinite reflux and an infinite number of trays has relevant implications for columns operating at finite reflux and with a finite number of trays. Using numerically constructed bifurcation diagrams for specific examples,
we show that these multiplicities tend to vanish for small columns and/or for low reflux flows. Finally, we comment on the effect of multiplicities on column design and operation for some specific examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8edfz-hwm97Model Predictive Control: Multivariable Control Technique of Choice in the 1990s?
https://resolver.caltech.edu/CaltechCDSTR:1993.024
Authors: {'items': [{'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}]}
Year: 1993
The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived powerful stability results for linear and nonlinear systems with and without constraints, for the nominal case and in the presence of model uncertainty. Some of these results are reviewed. Optimistic speculations about the future of MPC conclude the paper.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k1rqg-npx81Stability of Model Predictive Control with Soft Constraints
https://resolver.caltech.edu/CaltechCDSTR:1993.025
Authors: {'items': [{'id': 'Zheng-A', 'name': {'family': 'Zheng', 'given': 'A.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}]}
Year: 1994
We derive stability conditions for Model Predictive Control (MPC) with hard constraints on the inputs and "soft" constraints on the outputs for an infinitely long output horizon. We show that with state feedback MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback the eigenvalues must be strictly inside the unit circle. The on-line optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ay8yc-6cq77Constrained Stabilization of Discrete-Time Systems
https://resolver.caltech.edu/CaltechCDSTR:1993.023
Authors: {'items': [{'id': 'Balakrishnan-V', 'name': {'family': 'Balakrishnan', 'given': 'V.'}}, {'id': 'Zheng-A', 'name': {'family': 'Zheng', 'given': 'A.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}]}
Year: 1994
Based on the growth rate of the set of states reachable with unit-energy inputs, we show that a discrete-time controllable linear system is globally controllable to the origin with constrained inputs if and only if all its eigenvalues lie in the closed unit disk. These results imply that the constrained Infinite-Horizon Model Predictive Control algorithm is globally stabilizing for a sufficiently large number of control moves if and only if the controlled system is controllable and all its eigenvalues lie in the closed unit disk.
In the second part of the paper, we propose an implementable Model Predictive Control algorithm and show that with this scheme a discrete-time linear system with n poles on the unit disk (with any multiplicity) can be globally stabilized if the number of control moves is larger than n. For pure integrator systems, this condition is also necessary. Moreover, we show that global asymptotic stability is preserved for any asymptotically constant disturbance entering at the plant input.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vemjp-3n995Estimation of Cross Directional Properties: Scanning versus Stationary Sensors
https://resolver.caltech.edu/CaltechCDSTR:1994.002
Authors: {'items': [{'id': 'Tyler-M-L', 'name': {'family': 'Tyler', 'given': 'M. L.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}]}
Year: 1994
Periodic time varying Kalman filter calculations for problems involving scanning sensors are solved using "lifting" techniques common for multirate systems. The solution of this problem is used to compare the performance of scanning sensors versus stationary sensors in the estimation of cross directional properties. Furthermore, we examine controller performance when the outputs from the Kalman filter are used as inputs to a state feedback control law. Although adding sensors may significantly enhance the estimates of cross directional properties, feedback of these improved estimates may translate to lower levels of improvement in cross directional variations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1trgf-1xz34Design and Operational Modifications to Model IV FCCUs to Improve Dynamic Performance
https://resolver.caltech.edu/CaltechCDSTR:1994.007
Authors: {'items': [{'id': 'Huq-I', 'name': {'family': 'Huq', 'given': 'Iftikhar'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Sorensen-R', 'name': {'family': 'Sorensen', 'given': 'Ronald'}}]}
Year: 1994
Model IV Fluid Catalytic Cracking Units (FCCUs) differ from other cracking units in that model IV FCCUs do not have slide valves in the catalyst circulation lines to enable direct control of catalyst circulation rate through the unit. Reducing fluctuations in catalyst circulation rate is found to significantly improve closed loop performance of the FCCU. Some design and operational modifications that can be made to model IV FCCUs to improve closed loop performance at the regulatory level based on this insight are modeled and compared. Closed loop performance of a model IV FCCU operated with the weir and standpipe always flooded is examined. The achievable performance is significantly better than that of the standard model IV FCCU. The closed loop performance of the model IV FCCU modified to incorporate slide valves in the catalyst circulation lines is also examined. The performance of the FCCU with slide valves is better than the performance achievable by the FCCU with the weir flooded. It is found that model IV FCCUs are ill-conditioned owing to the use of the weir and standpipe arrangement in the regenerator section. Both the operational and design modifications studied reduce plant ill-conditioning appreciably.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tae2e-xwm17Optimal and Robust Design of Integrated Control and Diagnostic Modules
https://resolver.caltech.edu/CaltechCDSTR:1994.008
Authors: {'items': [{'id': 'Tyler-M-L', 'name': {'family': 'Tyler', 'given': 'Matthew L.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1994
The problem of designing an integrated control and diagnostic module is considered. The four degree of freedom controller is recast into a general framework wherein results from optimal and robust control theory can be easily implemented. For the case of an H2 objective, it is shown that the optimal control-diagnostic module involves constructing an optimal controller, closing the loop with this controller, and then designing an optimal diagnostic module for the closed loop. When uncertain plants are involved, this two-step method does not lead to reasonable diagnostics, and the control and diagnostic modules must be synthesized simultaneously. An example shows how this design can be accomplished with available methods.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x3s1m-qsp46Computational complexity of μ calculation
https://resolver.caltech.edu/CaltechAUTHORS:BRAieeetac94
Authors: {'items': [{'id': 'Braatz-R-P', 'name': {'family': 'Braatz', 'given': 'Richard P.'}}, {'id': 'Young-P-M', 'name': {'family': 'Young', 'given': 'Peter M.'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1994
DOI: 10.1109/9.284879
The structured singular value μ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/exyey-rws55Achievable closed-loop properties of systems under decentralized control: conditions involving the steady-state gain
https://resolver.caltech.edu/CaltechAUTHORS:CAMieeetac94
Authors: {'items': [{'id': 'Campo-P-J', 'name': {'family': 'Campo', 'given': 'Peter J.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Mafred'}}]}
Year: 1994
DOI: 10.1109/9.284869
The question of the existence of decentralized controllers for open-loop stable multivariable systems which provide particular closed-loop properties is investigated. In particular, we study the existence of decentralized controllers which provide integral action (Type I closed-loop performance) and also demonstrate one or more of: unconditional stability, integrity with respect to actuator and sensor failure, and decentralized unconditional stability. Necessary, sufficient, and, in some cases, necessary and sufficient conditions on the open-loop steady-state gain are derived such that there exists a controller which provides these desired closed-loop characteristics. These results provide the basis for a systematic approach to control structure selection for decentralized controller design.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t76gc-78r43Multiple Steady States in Heterogeneous Azeotropic Distillation
https://resolver.caltech.edu/CaltechCDSTR:1994.012
Authors: {'items': [{'id': 'Bekiaris-N', 'name': {'family': 'Bekiaris', 'given': 'Nikolaos'}}, {'id': 'Meski-G-A', 'name': {'family': 'Meski', 'given': 'George A.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1994
In this article we study multiple steady states in ternary heterogeneous azeotropic distillation. We show that in the case of infinite reflux and an infinite number of trays one can construct bifurcation diagrams on physical grounds with the distillate flow as the bifurcation parameter. Multiple steady states exist when the distillate flow varies non-monotonically along the continuation path of the bifurcation diagram. We show how the distillate and bottom product paths can be located for tray or packed columns, with or without decanter and with different types of condenser and reboiler. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the product paths. We also locate in the composition triangle the feed compositions that lead to these multiple steady states. We show that the prediction of the existence of multiple steady states in the case of infinite reflux and an infinite number of trays has relevant implications for columns operating at finite reflux and with a finite number of trays.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gqm4s-z7r92Minimizing the Euclidean Condition Number
https://resolver.caltech.edu/CaltechAUTHORS:20120229-153642155
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1994
DOI: 10.1137/S0363012992238680
This paper considers the problem of determining the row and/or column scaling of a matrix A that minimizes the condition number of the scaled matrix. This problem has been studied by many authors. For the cases of the ∞-norm and the 1-norm, the scaling problem was completely solved in the 1960s. It is the Euclidean norm case that has widespread application in robust control analyses. For example, it is used for integral controllability tests based on steady-state information, for the selection of sensors and actuators based on dynamic information, and for studying the sensitivity of stability to uncertainty in control systems.
Minimizing the scaled Euclidean condition number has been an open question—researchers proposed approaches to solving the problem numerically, but none of the proposed numerical approaches guaranteed convergence to the true minimum. This paper provides a convex optimization procedure to determine the scalings that minimize the Euclidean condition number. This optimization can be solved in polynomial-time with off-the-shelf software.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/77k80-98q27Performance Monitoring of Control Systems using Likelihood Methods
https://resolver.caltech.edu/CaltechCDSTR:1995.007
Authors: {'items': [{'id': 'Tyler-M-L', 'name': {'family': 'Tyler', 'given': 'Matthew L.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1995
Evaluating deterioration in performance of control systems using closed loop operating data is addressed. A framework is proposed in which acceptable performance is expressed as constraints on the closed loop transfer function impulse response coefficients. Using likelihood methods, a hypothesis test is outlined to determine if control deterioration has occurred. The method is applied to a simulation example as well as data from an operational distillation column, and the results are compared to those obtained using minimum variance estimation approaches.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bx8cf-nwk39Robust Constrained Model Predictive Control using Linear Matrix Inequalities
https://resolver.caltech.edu/CaltechCDSTR:1995.011
Authors: {'items': [{'id': 'Kothare-M-V', 'name': {'family': 'Kothare', 'given': 'Mayuresh V.'}}, {'id': 'Balakrishnan-V', 'name': {'family': 'Balakrishnan', 'given': 'Venkataramanan'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1995
The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t7km1-0q967Identification of Uncertainty Bounds for Robust Control with Applications to a Fixed Bed Reactor
https://resolver.caltech.edu/CaltechAUTHORS:20180316-124527093
Authors: {'items': [{'id': 'Webb-C-J', 'name': {'family': 'Webb', 'given': 'Christopher J.'}}, {'id': 'Budman-H-M', 'name': {'family': 'Budman', 'given': 'Hector M.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1995
DOI: 10.1021/ie00044a026
A model-based robust controller is designed for a packed bed methanation reactor. To accomplish
this objective, model uncertainty bounds are identified from experimental data. A physically
motivated methodology of "regions mapping" was developed to compute the uncertainty bounds
in the complex plane. This technique is compared to other existing nonparametric approaches
for a simple nonlinear system and is shown to produce a more accurate description of the model
uncertainty for the purpose of robust control design. This "regions-mapping" approach is then
applied to a fixed bed reactor and uncertainty bounds are computed. A robust controller with
a single adjustable parameter is designed for the reactor using internal model control (IMC)
theory. The computed uncertainty bounds are experimentally validated using the IMC controller.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/80mvw-2c226Multiple Steady States in Heterogeneous Azeotropic Distillation
https://resolver.caltech.edu/CaltechAUTHORS:20170809-101639023
Authors: {'items': [{'id': 'Bekiaris-N', 'name': {'family': 'Bekiaris', 'given': 'Nikolaos'}}, {'id': 'Meski-G-A', 'name': {'family': 'Meski', 'given': 'George A.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1996
DOI: 10.1021/ie940493e
In this article, we study multiple steady states in ternary heterogeneous azeotropic distillation. We show that in the case of infinite reflux and an infinite number of trays, one can construct bifurcation diagrams on physical grounds with the distillate flow as the bifurcation parameter. Multiple steady states exist when the distillate flow varies nonmonotonically along the continuation path of the bifurcation diagram. We show how the distillate and bottom product paths can be located for tray or packed columns, with or without decanter and with different types of condenser and reboiler. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the product paths. We also locate in the composition triangle the feed compositions that lead to these multiple steady states. We show that the prediction of the existence of multiple steady states in the case of infinite reflux and an infinite number of trays has relevant implications for columns operating at finite reflux and with a finite number of trays.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c92a1-bbs68Multiplier theory for stability analysis of anti-windup control systems
https://resolver.caltech.edu/CaltechCDSTR:1996.012
Authors: {'items': [{'id': 'Kothare-M-V', 'name': {'family': 'Kothare', 'given': 'Mayuresh V.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1996
We apply the passivity theorem with appropriate choice of multipliers to develop sufficient conditions for stability of the general anti-windup bumpless transfer (AWBT)
framework presented in [24]. For appropriate choices of the multipliers, we show that these tests can be performed using convex optimization over linear matrix inequalities (LMIs). We show that a number of previously reported attempts to analyze stability of AWBT control systems, using such well-known and seemingly diverse techniques as the Popov, Circle and Off-Axis Circle criteria, the optimally scaled small-gain theorem (generalized μ upper bound) and describing functions, are all special cases of the general
conditions developed in this paper. The sufficient conditions are complemented by necessary conditions for internal stability of the AWBT compensated system. Using
an example, we show how these tests can be used to analyze the stability properties of a typical anti-windup control scheme.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vmvyn-q3j62"Linearizing" Controller Design for a Packed-Bed Reactor Using a Low-Order Wave Propagation Model
https://resolver.caltech.edu/CaltechAUTHORS:20170809-100110031
Authors: {'items': [{'id': 'Doyle-F-J-III', 'name': {'family': 'Doyle', 'given': 'Francis J., III'}}, {'id': 'Budman-H-M', 'name': {'family': 'Budman', 'given': 'Hector M.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1996
DOI: 10.1021/ie9404083
A nonlinear controller design for a packed-bed reactor is presented. The scheme employs a two-tier approach in which, first, a low-order nonlinear model is developed and, subsequently, a feedback linearizing control law is synthesized. The reduced-order model treats transport mechanisms in the reactor as a nonlinear wave which propagates through the bed. Application of input−output "linearizing" control yields linear dynamics over a wide range of operating conditions. The practical issues of implementing the resultant digital, implicit, nonlinear control law on an actual system are addressed. Closed-loop simulations are used to illustrate the robustness properties of the nonlinear controller. In addition, the relative strengths of this approach over traditional linear control are identified.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7ataz-mee49Multiple Steady States in Distillation: ∞/∞ Predictions, Extensions, and Implications for Design, Synthesis, and Simulation
https://resolver.caltech.edu/CaltechAUTHORS:20180524-154556596
Authors: {'items': [{'id': 'Bekiaris-N', 'name': {'family': 'Bekiaris', 'given': 'Nikolaos'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1996
DOI: 10.1021/ie950450d
Bekiaris et al. (1993, 1996) presented a thorough study of the existence of multiple steady states in homogeneous and heterogeneous ternary azeotropic distillation based on the analysis of the case of infinite reflux and an infinite number of trays (∞/∞ case). In this paper, first we show how the ∞/∞ analysis and predictions can be extended to quaternary mixtures. Next, the implications of these multiplicities for column design, synthesis, and simulation are demonstrated. More specifically, we show how the ∞/∞ predictions can be useful for the selection of the entrainer, the equipment, and the separation scheme. We show that, in some cases, the column operation at an unstable steady state may have some advantages. The important issue of the effect of the thermodynamic phase equilibrium on the existence of multiplicities is discussed. Using the ∞/∞ analysis, we identify entire mixture classes for which multiplicities are inherent and robust. Mixtures with ambiguous VLE data are studied; we show that in some cases a slight VLE difference between models and/or experimental data may affect the existence of multiplicities while other, major VLE discrepancies do not. Finally, we identify the key issues and the pitfalls one should be cautious about when designing or computing the composition profile of an azeotropic distillation column with a commercial simulator.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6mem6-r4v25Identification of low order manifolds: Validating the algorithm of Maas and Pope
https://resolver.caltech.edu/CaltechAUTHORS:RHOchaos99
Authors: {'items': [{'id': 'Rhodes-C', 'name': {'family': 'Rhodes', 'given': 'Carl'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Wiggins-S', 'name': {'family': 'Wiggins', 'given': 'Stephen'}}]}
Year: 1999
DOI: 10.1063/1.166398
The algorithm of Maas and Pope (1992) is presented as a method for identification of invariant reduced-order manifolds for stable systems which exhibit dynamics with a time-scale separation. While this method has been published previously in the literature, theoretical justification for the algorithm was not presented in the original work. Here, it will be shown rigorously that the algorithm correctly identifies the slow manifold. Before the theoretical results are presented, a brief background on the behavior of singularly perturbed systems is presented. The algorithm of Maas and Pope (1992) is then introduced. This method will be applied to two different examples, a distillation column and a two-phase chemical reactor. For each of these examples, the resulting reduced-order description will be compared to other standard methods of producing reduced-order models. In addition, some preliminary thoughts on how this method can be used to form reduced-order models are presented.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h77kc-svy81Wearable Neural Prostheses - Restoration of Sensory-Motor Function by Transcutaneous Electrical Stimulation
https://resolver.caltech.edu/CaltechAUTHORS:20110331-140302044
Authors: {'items': [{'id': 'Micera-S', 'name': {'family': 'Micera', 'given': 'Silvestro'}}, {'id': 'Keller-T', 'name': {'family': 'Keller', 'given': 'Thierry'}}, {'id': 'Lawrence-M', 'name': {'family': 'Lawrence', 'given': 'Marc'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Popovic-D-B', 'name': {'family': 'Popovic', 'given': 'Dejan B.'}}]}
Year: 2010
DOI: 10.1109/MEMB.2010.936547
In this article, we focus on the least invasive interface: transcutaneous ES (TES), i.e., the use of surface electrodes as an interface between the stimulator and sensory-motor systems. TES is delivered by a burst of short electrical charge pulses applied between pairs of electrodes positioned on the skin. Monophasic or charge-balanced biphasic (symmetric or asymmetric) stimulation pulses can be delivered. The latter ones have the advantage to provide contraction force while minimizing tissue damage.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dg26b-8p689