Kenneth R. Muske

The stability of constrained receding horizon control

An infinite horizon controller that allows incorporation of input and state constraints in a receding horizon feedback strategy is developed. For both stable and unstable linear plants, feasibility of the contraints guarantees nominal closed-loop stability for all choices of the tuning parameters in the control law. The constraints feasibility can be checked efficiently with a linear program. It is always possible to remove state constraints in the early portion of the infinite horizon to make them feasible. The controllers implementation requires only the solution of finite-dimensional quadratic programs. >

Nonlinear Model Predictive Control: A Tutorial and Survey

Abstract This paper presents a tutorial survey of model predictive control for constrained linear plants and nonlinear plants. A streamlined implementation is presented for constrained linear systems. The formulation is shown to be nominally stabilizing in the presence of constraints provided inconsistent state constraints are relaxed. Cases with incomplete state measurement and nonzero set points are also discussed. A constant output disturbance model is shown to provide offset free integral control. The differences between optimal control and model predictive control are illustrated with a stochastic control example. Nominal stability is proved for a class of nonlinear plants. The major topics of current research in the field are summarized.

Linear model predictive control of unstable processes

Abstract This paper discusses the implementation of linear model predictive control techniques with open-loop unstable models. These models come from unstable plants and stable plants with conditionally stable disturbance models. The regulator is based on a quadratic performance criterion subject to input and state constraints. It is shown to be nominally stabilizing for all positive definite penalties on the input, positive semi-definite penalties on the output, and feasible constraints. Robust stability of the unconstrained regulator is also discussed. The case of incomplete state measurement is addressed with state estimation. The state is estimated from output measurements using the standard linear observer formulation. It is shown that the interconnection of a stable observer and the constrained regulator guarantees a nominally stabilizing controller.

Disturbance model design for linear model predictive control

Model predictive control (MPC) algorithms typically use a constant output bias for feedback, which can be interpreted by assuming that a constant disturbance perturbs the process output. This assumption leads to sluggish rejection of most real unmeasured disturbances since these disturbances generally enter the loop through state or input channels. An improved performance is often possible by designing an unmeasured disturbance model that explicitly incorporates input and state disturbance effects. A Kalman filter can then be employed to estimate the disturbances, allowing the control algorithm to reject them more quickly. This paper presents design guidelines for a disturbance model that accommodates unmeasured disturbances entering through the process input, state, or output. Conditions that guarantee detectability of the augmented system model are provided. A simulation example illustrates the performance benefits possible through this approach.

The stability of constrained receding horizon control with state estimation

A stable, constrained, receding horizon, state feedback regulator combined with a stable state estimator is presented and shown to be asymptotically stable. The regulator is a discrete time, infinite horizon formulation that allows the incorporation of both state and input constraints. The state estimator is any stable discrete time linear observer.

Implementable model predictive control in the state space

Model predictive control is an optimal control based method for constrained feedback control. Previous work at The University of Texas at Austin has focussed on the development of model predictive controllers that are nominally asymptotically stable for all valid tuning parameters. This development eliminated the need for tuning to obtain nominal stability. However, some implementation issues were not addressed. This work provides a discussion of those issues and solutions that allow the application of a nominally stable linear model predictive controller to be more easily realized in practice. The algorithms discussed in this work are implemented using Octaves (1993) high level interactive language and can be easily translated into other programming languages.

Dynamic cellular modeling for continuous fermentation

This paper presents the results of an experimental study intended to compare dynamic process modeling techniques for a continuous fermentation system. We consider a lumped parameter parametric model based on the ideal chemostat and a nonparametric empirical Volterra series model. We compare the dynamic cell mass predictions from each model form to that obtained experimentally for a complex Escherichia coli fermentation system and discuss the results.

Implementation of advanced process control-perspectives from academia

A successful collaboration between academia and industry in the implementation of advanced process control is one that develops new theory or methodology and also addresses a relevant industrial problem. Collaboration can provide significant benefits to an academic research group. However, there are a series of issues that must be addressed for the interaction to be successful. These benefits and issues are discussed in this paper.