This paper describes a simple "high-level" controller called a "supervisor" which is capable of switching into feedback with a SISO process, a sequence of linear positioning or set-point controllers from a family of candidate controllers so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by a SISO linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the positioning problem if the transfer function of the process were to be one of the subclasses' members. Each subclass contains a "nominal process model transfer function" about which the subclass is centred. It is shown that in the absence of unmodeled process dynamics, the proposed supervisor can successfully perform its function even if process disturbances are present, provided they are bounded and constant.

Supervisory control of families of linear set-point controllers - Part I. Exact matching

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), H/sub 2/ and H/sub /spl infin//, optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed.

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Distributed control of spatially invariant systems

Between the well-studied areas of discontinuous control [1], [2] on the one hand and sampled data control [3] on the other lies the largely unexplored area of logic-based switching control systems. By a logic-based switching controller is meant a controller whose subsystems include not only familiar dynamical components {integrators, summers, gains, etc.} but logic-driven elements as well {e.g., [4]}. More often than not the predominately logical component within such a system is called a supervisor [5], a mode changer [6], a gain scheduler, or something similar. Within the last decade a number of analytical studies of such systems have emerged, mainly in the area of self-adjusting control [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. These studies and others have shown that much can be gained by using logic-based switching together with more familiar techniques in the synthesis of feedback controls. The overall models of systems composed of such logics together with the processes they are intended to control are concrete examples of hybrid dynamical systems [17, 18, 19]. The aim of this paper is to give a brief tutorial review of four different classes of hybrid systems of this type — each consists of a continuous-time process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic.

Control Using Logic-Based Switching

http://portal.research.lu.se/portal/files/4879107/8727216.pdf

Drum-boiler dynamics

This paper describes a nonlinear dynamic model for natural circulation drum-boilers. The nonlinear model which is intended for model based control focuses on the complicated dynamics ofthe drum, downcomer, and riser components. A strong effort has been made to strike a balance between fidelity and simplicity. The model is derived from first principles, and is characterized by a few physical parameters. Results from validation of the model against unique plant data are presented. The model captures the shrink and swell effect very well. It also describes the behavior of the system over a wide operating range.

Drum-Boiler Dynamics

Uniformly optimal control of linear time-invariant plants: Nonlinear time-varying controllers

Robust stabilization of distributed systems

The objective of this paper is to study in detail stabilizability and stable-proper factorizations for linear time-varying discrete-time systems. Our main results are: (i) If a linear-time-varying system can be stabilized by dynamic state feedback, then it can also be stabilized by memoryless state feedback. (ii) A complete characterization of the existence of stable-proper factorizations for linear time-varying input/output operators. This characterization is nontrivial; there exist input/output operators that do not admit stable-proper factorizations.

Stabilizability and stable-proper factorizations for linear time-varying systems

The authors present several algorithms that compute approximate solutions to the Lyapunov equation AX+XA/sup T/+BB/sup T/=0 and the algebraic Riccati equation A/sup T/X+XA-XBR/sup -1/ B/sup T/X+C/sup T/C=0, where A is large and sparse and B and C are low rank. In particular, they test the Krylov subspace approximation and reduced rank integration for the Riccati equation. Although the algorithms are heuristically good, no convergence proofs are as yet available. >

Heuristic approaches to the solution of very large sparse Lyapunov and algebraic Riccati equations

In this paper we present a new approach to adaptive robust control. The essential idea involved is to fragment modeling uncertainty in a physical plant into "small" families of plant models for which robust LTI controllers can be readily designed. We then implement a convex combination of these controllers, the parameters of which are tuned based on error measurements. Using this approach we are able to provide absolute bounds on the ability to adaptively stabilize against unmodeled dynamics.

Kameshwar Poolla

Papers

Uniformly optimal control of linear time-invariant plants: Nonlinear time-varying controllers

Robust stabilization of distributed systems

Stabilizability and stable-proper factorizations for linear time-varying systems

Heuristic approaches to the solution of very large sparse Lyapunov and algebraic Riccati equations

Adaptive Robust Control: A New Approach