Synthesis of multivariable PID control systems based on the estimation of output derivative

This paper is concerned with the synthesis problem of multivariable proportional-integral-derivative (PID) controllers based on the estimation of derivative of measured output. First, the mathematical model of linear plant and PID controller is given. An observer to estimate the output derivative appearing in PID controller is considered. Secondly, the problem of obtaining gains of both PID controller and observer under H_infin criterion is formulated as linear matrix inequality (LMI) one. Finally, a numerical example is given to verify the effectiveness of the presented approach.