On the design of multivariable PID controllers via LMI approach. (Q5960322)

PID control of multivariable high order plants is considered in this paper. The basic idea is to transform the problem of PID controller design to that of Static Output Feedback (SOC) controller design. In section 2, the method of transformation is demonstrated. Once SOC is solved, the PID controller gains will be recovered on the assumption that a certain matrix is invertible. Problems of stabilization, \(H_2\) performance spec, \(H_\infty\) performance spec, and Maximum Output Control (MOC) are studied in sections 3, 4, 5, and 6, respectively. In each problem, the existence condition of SOC solution is expressed in the form of LMI. Solving LMI (if the solution exists) by iteration method is demonstrated in each case. A numerical example is shown in section 7.