Low-complexity constrained control of the opposed current converter using quadratic control contractive sets

Abstract

The opposed current converter (OCC) is a highprecision power amplifier that does not require blanking time in between switching and hence has high output quality. Like most of industrial power amplifiers, OCCs are typically controlled by classical control methods, which are simple and able to guarantee certain local optimality. However, physical constraints of the system are often neglected in the classical control design, which might lead to unreliable operation. More advanced control methods that can handle constraints are often of high complexity. This paper proposes an explicit control design method for the OCC based on a sequence of quadratic control contractive sets. The proposed controller can be computed by a single linear matrix inequality. It is proven to guarantee stability, locally optimal performance, constraints satisfaction and it has low complexity. Experimental results on a prototype OCC demonstrate the effectiveness of the proposed method.

Fast and scalable constrained reference tracking for discrete-time linear systems

“…Then, a sequence of quadratic control contractive sets is employed inspired by the fact that quadratic sets can be synthesized by simple linear matrix inequalities (LMIs). A similar approach has been proposed in literature for constrained stabilization, see e.g., [11]- [13]. However, the method proposed in this paper do not impose that the resulting sets are one-step controllable sets as proposed in [12], [13] and also does not use a sequence of predetermined points as in [11].…”

“…Moreover, comparing with the solution from [13], we can obtain a larger outer set using less sets because we do not impose that all states inside Q l+1 should be driven in the set Q l in one step. Thus, we can efficiently solve Problem III.1 also for highdimensional systems since the existing SDP solvers can solve reasonably large scale problems, see e.g., [15].…”

“…It should be noted that using (13) all quadratic sets are µ-contractive. Therefore, we obtain inherent robustness to perturbations to the size (1 − µ)Q l .…”

“…In the first step we assign to each set a linear control law and we compute the sequence of contractive sets and corresponding linear control laws. The derivation of the solution for the first step involves a series of matrix manipulations, similarly as used in [13] to obtain a convex optimization problem in the form of LMIs. In what follows we provide the details of the derivation for completeness.…”