A tool to analyze robust stability for model predictive controllers

Santos, Lino O.; Biegler, Lorenz T.

doi:10.1016/s0959-1524(98)00045-6

Cited by 20 publications

(26 citation statements)

References 25 publications

(33 reference statements)

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“…Here, we develop a framework that can be used to evaluate off-line, the closed-loop robustness of a constrained MPC system in the presence of plant/model mismatch. This is a direct extension of previous work on the unconstrained case [10] for the discrete state feedback problem. Both the plant and model are described using nonlinear state-space models.…”

Section: Introductionmentioning

confidence: 65%

“…where rðs Ã iþk ; e Ã iþk ; nÞ denotes a vector whose elements are nonlinear functions of s Ã iþk , e Ã iþk and n. Following the same developments as in Santos and Biegler [10] we obtain…”

Section: Preliminariesmentioning

confidence: 95%

“…To extend the analysis made for the unconstrained case by Santos and Biegler [10] to (11)- (13) we use an exact penalty formulation as developed by Oliveira and Biegler [8]. This approach converts (11)-(13) to the problem P q ðx i Þ:…”

Section: Stability Analysismentioning

confidence: 99%

“…Proceeding as in the unconstrained case study by Santos and Biegler [10] with Ç * (AE) replacing W * (AE) we derive the following bound on the mismatch term:…”

Section: Preliminariesmentioning

confidence: 99%

“…There a robustness margin is derived in conjunction with the Lyapunov stability conditions. A related analysis is also presented for unconstrained nonlinear MPC problems in [10]. On the other hand, the treatment of constrained MPC systems is more difficult, and in [6,5] a robust analysis is presented based on Pontryagin difference sets, which can lead to conservative controllers.…”

Section: Introductionmentioning

confidence: 99%

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A tool to analyze robust stability for constrained nonlinear MPC

Santos¹,

Biegler²,

Castro³

2008

Journal of Process Control

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A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.

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Section: Introductionmentioning

confidence: 65%

Section: Preliminariesmentioning

confidence: 95%

Section: Stability Analysismentioning

confidence: 99%

“…Proceeding as in the unconstrained case study by Santos and Biegler [10] with Ç * (AE) replacing W * (AE) we derive the following bound on the mismatch term:…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A tool to analyze robust stability for constrained nonlinear MPC

Santos¹,

Biegler²,

Castro³

2008

Journal of Process Control

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Dynamic Modeling and Simulation for Robust Control of Distributed Processes and Bioprocesses

Alonso¹,

García²,

Vilas³

2010

Process Systems Engineering

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370 11 Dynamic Modeling and Simulation for Robust Control dimensional space of particle positions and velocities into a reduced order formulation which usually takes the form of the Boltzmann equation. Finally, coarse graining methods will zoom out the view point of the system and take the description back to the mesoscopic and macroscopic world of continuum [29].One conclusion to be drawn from this picture is that for any given time and length scales there will be a number of states dynamically active, coupled with others either relaxed (those states active at shorter scales) or frozen (as they are associated with much slower dynamics). Mathematically, such description translates into a highly coupled stiff system obeying a nonlinear set of algebraic, partial, and ordinary differential equations, which is usually difficult to solve. In this way, the stiffness of the resulting problem is the effect of the diversity of time scales coexisting in the system. From a control point of view or even from the more general perspective of "decision making," stiffness must be avoided, what calls for model reduction methods able to provide the simplest robust dynamic description representative of the system at the scales of interest.The application to process control should be considered not just in the restricted sense of a PID regulator or any other such device equipped with a "compensation" rule which responds to deviations between the prescribed operation condition and the current one. From a broader perspective a controller consists of a virtual representation of the system one wants to operate (the plant), and a sort of agent which at regular time instants inspects the current state of the process and employs the system representation to screen future scenarios by asking whether a given decision should be made or not. Once the best possible action is found, the agent implements it in the real plant and waits for the response given by the sensors to initiate further corrective actions. This logic, properly repeated during the process operation, is what is known as a feedback control scheme. In its simple version a PID contains one such representation of the linear dynamic range, which in this case is explicitly inverted in some smart way as the internal model control (IMC) theory clearly highlights [39].More sophisticated control algorithms will also share the same construction logic, namely a virtual representation of the system dynamics, an agent devising future operation, and a comparison rule which evaluates the real effect of the control actions on the process. Such control methods would include adaptive control [41], feedback linearization control [34], slide mode control [48], or model predictive control (MPC) in all its flavors (linear, nonlinear, constrained, etc.) [23,32,42].In constructing a reliable dynamic representation for the system to be controlled, and depending on the class of description employed, there are a wide variety of methods at hand. However, they all rely on the very same basic principle, n...

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