P. Belanger

Computational experience with the solution of the matrix Lyapunov equation

This correspondence presents a comparative study of three methods for the numerical solution of the matrix Lyapunov equation. The test case is a 24th-order system with highly underdamped eigenvalues and a rather high degree of stiffness. The conclusions favor a method by Bartels and Stewart based on a reduction to Schur form of the A matrix.

Observation and control of linear systems with constant disturbances

The problem of regulation in the presence of a fixed but unknown disturbance is considered. The control law is designed as if the disturbance were known, and an estimate given by an observer is used in the control law. A system results having as many integrators as outputs.

A paper machine color control system design using modern techniques

This paper takes the reader through the steps of a control system design using both optimal control theory and sensitivity analysis. The problem is to control color on a paper machine. The physical aspects of color are briefly described and a model for the paper machine is given. The model responses are compared with responses obtained experimentally on a small-scale machine. The retention turns out to be an unknown and variable parameter. A sampled-data design is carried out for the nominal case where the retention is 100 percent using the linear-regulator theory. A parameter \rho weighing the control effort in the quadratic cost function is then used as a design parameter.

Design of low-order compensators by gain matching

A design procedure for low-order compensators is presented which attempts to use available system and dynamic compensator outputs to obtain a least-squares fit to the optimal full-state gain. The procedure is shown to converge and, at least for the examples presented, produces results at least good enough to serve as a starting point for a fixed-structure optimization procedure.

Application of dynamic optimization techniques to reactor control in the manufacture of ethylene

The formulation and solution of optimal control problems that arise in the study of an ethylene producing plant are discussed. Control problems are stated that involve a single pyrolysis reactor and a set of identical reactors operating in parallel. Typical dynamic optimization results are given, along with some thoughts on suboptimal control policies and performance sensitivity to process parameter variations. A new type of control problem is considered that involves constraints on control values that are separated in time by multiples of a constant time shift value.

Contribution to the solution of the linear-quadratic problem for large systems

The feasibility of using a previously published algorithm as a tool for the computation of the Kalman gain for large systems is demonstrated. Some aspects of its implementation and its numerical properties are explored. Numerical examples demonstrate the suitability of the algorithm for the computation of the optimal gain for very-high-order systems. The optimal gain is computed for a sparse system with 401 states. >

Equivalence of optimal fixed-order controllers

It has been shown by Sims and Melsa [1] that the system matrix of a fixed-order linear compensator may be chosen arbitrarily, so long as a proper choice of gain matrices follows. That result was derived using optimal control theory. The purpose of this communication is to trace the source of this phenomenon to the equivalence of time-varying controllers.