Robust PID controller based on closed-loop gain shaping algorithm and its application

The controlled plant is converted into a second order deep strictly proper plant through model reduction or Bode plot approximation, then all the parameters of robust PID controller can be got from theory using the first order closed-loop gain shaping algorithm, which constructs a robust controller by the four engineering parameters of the largest singular value, bandwidth frequency, peak value and slope of high frequency asymptote according to the desired shape of sensitivity function and closed-loop frequency spectrum. Through two simulating examples, it follows that the control performance and robust stability of robust PID controller are satisfactory. The robust PID algorithm is simple and easy to use in engineering.