A hybrid approach to the synthesis of simply structured robust and gain-scheduled controllers

Abstract

Abstract Frequently in engineering applications, simply structured controllers are required for plants whose dynamics are either not fully known or varies with time. The problem of designing such structurally constrained controllers is known to be NP-hard. This paper presents a method for designing such controllers for both continuous-time and discrete-time uncertain or linear parameter varying (LPV) systems. The method relies on sufficient linear matrix inequalities (LMI) conditions also presented here. These LMIs are used to evaluate performance of a given controller in terms of the worst-case induced L 2 -norm for complete operational envelope. The strength of this LMI formulation lies in the fact that the robust performance evaluation condition is less conservative than standard results because it is based on a parameter-dependent Lypunov function and full block multipliers which allows to consider a bound on the rate of change in parameters. The LMI conditions are used in a hybrid evolutionary-LMI algorithm. The proposed algorithm employs evolutionary search to span the solution space and LMI solvers to find the worst case performance. The algorithm is independent of the controller structure, which allows to design simply structured controllers for complex systems in a systematic way. To illustrate the approach, two applications are presented: a distillation column and a spark ignition (SI) engine. For the distillation column, simple PI controllers with first order pre-filters are designed to achieve time and frequency domain control objectives in the presence of 20% input uncertainty. For the SI engine example, gain-scheduled PID controllers are designed and tuned. these examples illustrate that the proposed approach can be used to systematically design simply structured low-order controllers, while satisfying all performance requirements in terms of the worst-case induced L 2 -norm.