Design of robust fractional-order controllers and prefilters for multivariable system using interval constraint satisfaction technique

Abstract

Design of robust controller for multivariable systems is very challenging and their automation is a key concern in control system design. In this paper, a new, simple, and reliable automated fractional-order multivariable Quantitative Feedback Theory (QFT) controllers design methodology is proposed. A fixed structure fractional-order multivariable QFT controller has been synthesized by solving QFT quadratic inequalities of robust stability and tracking specifications. The quadratic inequalities (constraints) are posed as Interval Constraint Satisfaction Problem (ICSP). The constraints are solved by constraint solver-RealPaver. The synthesis problem consists of obtaining a controller that ensures stability and meets a given set of performance specifications, in spite of disturbance and model uncertainties. In addition to perform the above tasks, a MIMO controller also has to perform the difficult task of minimizing interaction between the various control loops. Unlike existing manual or convex optimization based QFT design approaches, the proposed method gives a controller which meets all performance requirements in QFT, without going through the conservative and sequential design stages for each of the multivariable sub-systems. In the design method, we pose the prefilter design problem as an ICSP and solve it using the well-established constraint solver. The designed controllers and prefilters are tested for a quadruple tank process and their efficacy is demonstrated.