Reduced-order Design Research Articles

Integrated modeling and control for the Large Spacecraft Control Laboratory experiment facility

A software package which integrates model reduction and controller design is applied to design controllers for the Jet Propulsion Laboratory Large Spacecraft Control Laboratory experiment facility. Modal cost analysis is used for the model reduction, and various output covariance constraints are guaranteed by the controller design. The main motivation is to find the controller with the best performance with respect to output covariances. It is shown that by iterating on the reduced-order design model, the controller designed does have better performance than that obtained with the first model reduction, demonstrating an effective strategy for integrating modeling and control design.

Efficient Computation of the Solutions to Modified Lyapunov Equations

This paper develops a solution method for modified Lyapunov equations in which the modification term $\mathcal{F}( Q )$ is a linear function of the solution Q. Equations of this form arise in robustness analysis and in homotopy algorithms developed for solving the nonstandard Riccati and Lyapunov equations that arise in robust reduced-order design. The method relies on decomposing $\mathcal{F}( Q )$ as $\mathcal{F} ( Q ) = \mathcal{G} ( \phi ( Q ) )$, where $\phi ( Q )$ is an m-dimensional vector. It is shown that if m is small, the new solution procedure is much more efficient than are solution procedures based on a straightforward transformation of the modified Lyapunov equation to a linear vector equation in $n( n + 1 )/2$ unknowns. The results are extended to develop an efficient procedure for computing the solutions to an arbitrary number of coupled Lyapunov equations in which the coupling terms are linear operators.

Parameter-robust control design using a minimax method

A controller design method is presented that gives the best linear-quadratic-Gaussian closed-loop performance over a set of worst plant parameter changes. The design algorithm combines a multiplant optimal design code, SANDY, with a new worst parameter algorithm that uses a quadratic norm on parameter changes. The minimax algorithm is unique in the way it weights worst plants to expand the stable region in the parameter space. The method is applied to a two-mass/spring American Control Conference problem. A minimax controller is first designed for the case where the spring constant alone is uncertain. Next, several minimax controllers, including a reduced-order design, are synthesized for the benchmark problem where both masses and the spring constant are uncertain. The results show that minimax control provides near-optimal nominal performance with significant robustness and parameter margin improvements.

Linear control of nearly singularly perturbed hydropower plants

In this paper we consider a special class of linear control systems represented by the standard singularly perturbed system matrix and with the control input matrix having three different nonstandard forms. Many real systems (such as hydropower plants, systems with only few actuators) possess the control structure studied in this paper. The obtained results are quite simplified (comparing to the standard singularly perturbed control systems), and in one case the optimal solution of the algebraic Riccati equation is completely determined in terms of the reduced-order algebraic Lyapunov equations. The proposed method is successfully applied to the reduced-order design of optimal controllers for the real hydropower plant of the Serbian power system.

Reduced Order Design of Active Suspension Control

The presence of fast and slow modes in suspension systems is utilized in the design of two reduced-order active suspension control strategies. The first strategy is obtained by combining the solutions of slow and fast control sub-problems. The second strategy is based on a two-level hierarchical control design. The local level requires measurements of local fast variables, namely the unsprung mass velocities. The coordinating level relies on measurements of slow variables, namely, suspension deflections, sprung mass velocity, and mass pitch rate. Neither strategy requires tire deflection measurements. In spite of their simplified structure, simulation results indicate that their performance is comparable to that of the full-state feedback design.

LQG control with an H/sup infinity / performance bound: a Riccati equation approach

An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered. The H/sup infinity / performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L/sub 2/ performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H/sup infinity /-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H/sup infinity /-constrained problem. Both full- and reduced-order design problems are considered with an H/sup infinity / attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A further note on the robustness of output feedback control methods to modeling errors

In an earlier note it was shown that designing a nonstrictly proper output feedback compensator using a model that neglects parasitic elements might lead to an unstable closed-loop system even when the neglected modes are asymptotically stable. The purpose of this note is to show that this instability phenomenon might take place even when the reduced-order design model is strictly proper.

Input/Output Properties of Adaptive Control Systems: Robustness and Reduced Order Design

The question is examined of when an adaptive control system is robust to unmodeled dynamics and unknown bounded disturbances. Conditions are presented that ensure the existence of such robustness properties, but only locally; i.e., restrictions are placed on the behavior of signals in the ideal, perfectly tuned adaptive system. Local L∞-stability is investigated when certain tuned signals are assumed to be persistently exciting.

Pole-placement design of multiple controller systems via weak and strong controllability†

For linear time invariant systems, the notion of weal: and strong controllability is introduced using an eigenvalue sensitivity analysis. In systems with multiple controllers, the modes of the systems can be assigned to dh erent controllers according to this relative measure of controllability. Using this decomposition, a procedure for reduced-order polo-placement design is proposed.