Juan F. Camino

A convexifying algorithm for the design of structured linear controllers

Addresses the design of linear controllers with special structure imposed on the gain matrix. This problem is called a SLC (structured linear control) problem. The SLC problem includes fixed order output feedback control, decentralized control, joint plant and control design, and many other linear control problems. A theoretical framework that allows one to pursue the solution of SLC problems is provided. Although the obtained conditions are nonconvex, it is shown that solving a SLC problem involving standard control objectives such as stability, bounds on the H/sub 2/ or H/sub /spl infin// norms, and real positiveness is not harder than solving a standard unstructured static output feedback problem. A convexifying algorithm that might be used to solve the SLC problem is also developed. At each iteration a certain function is added to the constraints in order to make them convex. At convergence, the artificially introduced convexifying functions reduce to zero, guaranteeing the feasibility of the original problem. Local optimality can be guaranteed. Some examples illustrate how the SLC framework and the convexifying algorithm can improve the solutions of control problem with suboptimal solutions available.

Interpolation-Based Modeling of MIMO LPV Systems

This paper presents State-space Model Interpolation of Local Estimates (SMILE), a technique to estimate linear parameter-varying (LPV) state-space models for multiple-input multiple-output (MIMO) systems whose dynamics depends on multiple time-varying parameters, called scheduling parameters. The SMILE technique is based on the interpolation of linear time-invariant models estimated for constant values of the scheduling parameters. As the linear time-invariant models can be either continuous- or discrete-time, both continuous- and discrete-time LPV models can be obtained. The underlying interpolation technique is formulated as a linear least-squares problem that can be efficiently solved. The proposed technique yields homogeneous polynomial LPV models in the multi-simplex that are numerically well-conditioned and therefore suitable for LPV control synthesis. The potential of the SMILE technique is demonstrated by computing a continuous-time interpolating LPV model for an analytic mass-spring-damper system and a discrete-time interpolating LPV model for a mechatronic -motion system based on experimental data.

Interpolated Modeling of LPV Systems

This paper presents a new state-space model interpolation of local estimates technique to compute linear parameter-varying (LPV) models for parameter-dependent systems using a set of linear time-invariant models obtained for fixed operating conditions. The technique is based on observability and controllability properties and has three strong appeals, compared with the state of the art in the literature. First, it works for continuous-time as well as discrete-time multiple-input multiple-output systems depending on multiple scheduling parameters. Second, the technique is automatic to some extent, in the sense that, after the model selection, no user interaction is required at the different steps of the method. Third, the resulting interpolating LPV model is numerically well-conditioned such that it can be used for modern LPV control design. Moreover, the proposed technique guarantees that the local models have a coherent state-space representation encompassing existing results as a particular case. The benefits of the approach are demonstrated on a simulation example and on an experimental data set obtained from a vibroacoustic setup.

Interpolated Modeling of LPV Systems Based on Observability and Controllability

Abstract This paper presents a State-space Model Interpolation of Local Estimates (SMILE) technique to compute linear parameter-varying (LPV) models for parameter-dependent systems through the interpolation of a set of linear time-invariant (LTI) state-space models obtained for fixed operating conditions. Since the state-space representation of LTI models is not unique, a suitable coherent representation needs to be computed for the local LTI models such that they can be interpolated. In this work, this coherent representation is computed based on observability and controllability properties. It is shown that compared with the state of the art in the literature, this new method has three strong appeals: it is general, fully automatic and results in numerically well-conditioned LPV models. An example demonstrates the potential of the new SMILE technique.

AN APPLICATION OF INTERPOLATING GAIN-SCHEDULING CONTROL

Abstract This work investigates an application of interpolating gain-scheduling control for a structural acoustic problem. The dynamics of the system under consideration are highly sensitive to variation in the temperature. Therefore, linear time invariant ℋ 2 output feedback controllers are designed for different temperature conditions. Afterwards, these controllers are interpolated to provide a global discrete-time linear parameter-varying controller. The closed-loop stability is a posteriori guaranteed using recent less conservative analyses that consider bounds on the rate of variation of the temperature.

Gain-scheduled H ∞ -control of discrete-time polytopic time-varying systems

This paper presents synthesis procedures for the design of both robust and gain-scheduled H∞ static output feedback controllers for discrete-time linear systems with time-varying parameters. The parameters are assumed to vary inside a polytope and have known bounds on their rate of variation. The geometric properties of the polytopic domain are exploited to derive a finite set of linear matrix inequalities that consider the bounds on the rate of variation of the parameters. A numerical example illustrates the proposed approach.

Design of a vehicular suspension controller by static output feedback

A static output feedback controller is applied to the design of an active suspension model for a quarter-car vehicle, using only the suspension travel displacement and velocity as output variables. The feedback design proposed makes use of recent linear matrix inequalities results from the literature, also allowing to consider the presence of uncertain parameters. Simulations are carried out taking into account the model uncertainty. The results are shown to be as good as the classical linear quadratic regulator which supposes full state availability and precisely known parameters.

Solving matrix inequalities whose unknowns are matrices

This paper provides algorithms for numerical solution of convex matrix inequalities (MIs) in which the variables naturally appear as matrices. This includes, for instance, many systems and control problems. To use these algorithms, no knowledge of linear matrix inequalities (LMIs) is required. However, as tools, they preserve many advantages of the linear matrix inequality framework. Our method has two components: 1) a numerical (partly symbolic) algorithm that solves a large class of matrix optimization problems; 2) a symbolic ?Convexity Checker? that automatically provides a region which, if convex, guarantees that the solution from (1) is a global optimum on that region.

PLANT AND CONTROL DESIGN USING CONVEXIFYING LMI METHODS

Abstract This paper presents a methodology in the Linear Matrix Inequality (LMI) framework to jointly optimize the linear control law and the linear parameters in the plant. The paper solves an integrated plant and control design problem which bounds the covariance of selected outputs. The method simultaneously designs the plant parameters and the controller. The proposed method also allows one to guarantee bounds on the peak response in the presence of bounded energy excitations. With minor modifications, the method can also guarantee bounds on the H ∞ performance and many other convex performance criteria. The nonconvex problem is approximated by a convex one by adding a certain function to make the constraint convex. This “convexifying” function is updated with each iteration until the added convexifying function disappears at a saddle point of the nonconvex problem.

Multiobjective weighting selection for optimization-based control design

A methodology for the multiobjective design of controllers is presented, motivated by the problem of designing an active suspension controller. This problem has, as a particular feature, the possibility of being defined with two design variables only. The multiobjective controller is searched inside the space of optimal controllers defined by a weighted cost functional. The weightings are taken as the optimization variables for the multiobjective design. The method leads to (local) Pareto-optimal solutions and allows the direct specification of controller constraints in terms of some primary objectives which are taken into account in the multiobjective search.