Abstract
In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an H∞ mixed sensitivity approach. We first define the feasible controller parameter set, which is the set of the controller parameters that guarantee robust stability of the closed-loop system and the achievement of the nominal performance requirements. Then, thanks to Putinar positivstellensatz, we compute a convex relaxation of the original feasible controller parameter set and we formulate the original H∞ controller design problem as the non-emptiness test of a set defined by sum-of-squares polynomials. Two numerical simulations and one experimental example show the effectiveness of the proposed approach.
Highlights
The development of a worst-case control design for a linear plant subjected to unknown parameter uncertainties and disturbances has attracted the interest of the control community for many years
We propose a methodology to design a H∞ controller K(ξ, p) which guarantees robust stability to unstructured multiplicative uncertainty bounded by the function Wu(ξ), and fulfils the nominal performance defined through the weighting functions W1(ξ) and W2(ξ)
We present a unified approach to design for the H∞ mixed-sensitivity design for fixed structure robust controllers for both continuous time (CT) and discrete time (DT) systems
Summary
The development of a worst-case control design for a linear plant subjected to unknown parameter uncertainties and disturbances has attracted the interest of the control community for many years. In [11,12], discrete-time controllers are designed through the solution of two Riccati equations, while a convex optimization approach is proposed in [13]. Another Matlab toolbox for the design of fixed-structure controllers is Hinfstruct, which implements the algorithm proposed in [28] and is based on the Clarke sub-differential approach presented in [29] Both these Matlab packages are based on local optimization techniques, which have no guarantees about the convergence to the global optimal solution. We propose a unified framework to design continuous and discrete-time fixed structure controllers in the framework of the mixed-sensitivity approach. By exploiting Putinar positivstellensatz theorem [39], we formulate the H∞ mixed sensitivity controller design as the non-emptiness test of a convex set defined through a number of sum of squares (SOS) polynomial constraints.
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