Automated Synthesis of Robust QFT-PID Controllers based on Piecewise Linear Approximations

Quantitative feedback theory (QFT) is a frequency domain based robust control design techniques [1]. In this paper, the piecewise linear approximation based linear programming (PLA-LP) algorithms presented in [6] are extended for automatic synthesis of robust PID controller in the QFT framework. Firstly, the λ-formulations for the parallel or interacting form of the PID controller are derived. Then, the λ-formulations are incorporated into the QFT synthesis algorithm proposed in [6], and solved to global optimality using a mixed-integer programming (MIP) branch and bound solver. The proposed robust QFT-PID synthesis algorithm is demonstrated on two benchmark examples. Compared to existing methods, the PLA-LP based QFT-PID algorithm is faster by a couple of orders of magnitude, and also gives considerable reductions in the controller gain.