Reduced-order controller synthesis with regional pole constraint

Abstract

A reduced order output feedback controller is designed for a linear time invariant system, which guarantees that the closed-loop poles are placed within some pre-specified stability region in the complex plane. A convex approximation of the non-convex constraints is used to pose a sequence of semi-definite programs, which provide the lowest order proper controller satisfying the approximate constraints. The proposed method is demonstrated on two practical controller design applications.

Structured controller design for closed‐loop D ‐stability in convex/non‐convex regions: Mixed integer‐linear programming approach

“…In order to get rid of the logical ANDs in (6) and arrive at equivalent algebraic relations, assign five binary decision variables Figure 5. These binary decision variables are defined as the following:…”

“…This problem is still open even when the region is convex. A rather similar problem is studied in [18] where it is aimed to find a minimum order controller such that all poles of the MIMO feedback system are placed inside a pre-specified convex region. That study is based on the properties of polynomial matrices and has the advantage of being directly applicable to MIMO systems.…”

“…See, for instance, [2] and [3] where the problem of root clustering in parameter space is deeply studied and some applications are also presented. Robust D ‐stabilising controller design for an uncertain discrete‐time networked control system with time‐varying network‐induced delays [4], computation of state‐feedback gain matrix for a linear time‐invariant (LTI) system such that all the finite poles are placed within a pre‐defined stability region [5] and reduced‐order controller synthesis with regional pole constraint [6] are some other applications of D ‐stability.…”

“…FIGURE6 A sample mesh with four cells and the corresponding binary decision variables assigned to its nodes and cells…”

A variable gain state‐feedback technique for an AMD control system with stroke limit and its application to a high‐rise building

“…A robust control method with a regional PA constraint, which enhances both performance and robustness, has been widely studied. [ 26–28 ] There was a close relationship between the control gain and the strokes of the auxiliary mass. [ 29,30 ] Hence, in order to construct a practical system, a variable gain needs to be introduced to limit the stroke of the auxiliary mass and realize as a safety protection.…”