Automated synthesis of multivariable QFT controller using interval constraint satisfaction technique

Abstract

Robust controller synthesis of Multi-Input–Multi-Output (MIMO) systems is of great practical interest and their automation is a key concern in control system design. The synthesis problem consists of obtaining a controller that ensures stability and meets a given set of performance specifications, in spite of the disturbance and model uncertainties. In addition to perform the above tasks, a MIMO controller also has to perform the difficult task of minimizing the interaction between the various control loops.Unlike existing manual or convex optimization based Quantitative Feedback Theory (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 this paper, a new, simple, and reliable automated MIMO QFT controllers design methodology is proposed. A fixed structure MIMO 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 main feature of this method is that the algorithm finds all the solutions to within the user-specified accuracy. The designed MIMO QFT controllers are tested on the experimental setup designed by Educational Control Product (ECP) Magnetic Levitation Setup ECP 730. From the experimental results presented, it is observed that, the designed controller satisfies the desired performance specifications. It is also observed that, the interactions between the loops are within the specified limits. The robustness of the designed controllers are verified by putting extra weights on the magnets.