Simply structured controllers for parameter varying distributed systems

This paper presents a systematic approach to the synthesis of simply structured controllers for large scale parameter varying distributed systems. The design and optimization procedure consists of two loops. In an inner loop, an efficient LMI-based optimization algorithm is used to evaluate the closed-loop performance. The outer loop uses evolutionary operators to iteratively search for the parameters of a controller network that achieves the best performance. For the purpose of performance evaluation, new sufficient LMI conditions are presented to find the induced L2 norm of such systems. The conservatism of the analysis is reduced by the use of parameter dependent Lyapunov functions and by taking bounds on the parameter variation rates into account. Since the control algorithms are implemented on digital computers, the results are presented for discrete time and discrete space systems. The problem posed in this form is infinite dimensional, a gridding algorithm is also proposed to convert it into a finite dimensional problem. The approach is illustrated with two applications: active vibration control of a cantilever, and position control of a seismic cable. These examples illustrate that the performance analysis condition presented here is less conservative than previously presented LMI conditions. It is also demonstrated that the approach can be used to systematically design simply structured low-order controllers, while satisfying all performance requirements