Question

how to design linear PID controller via convex optimization?

(for first and second order system)

Answer 1

Explanation: The use of robust design techniques such as the one based on and for tuning proportional integral (PI) and proportional integral derivative (PID) controllers have been limited to address a small set of processes . This work addresses the problem by considering a wide set of possible plants , both first and second order continous -time systems with time delays and zeroes , leading to PI and PID controllers. The use of structered uncertainties to handle neglected dynamics allows to expand the range of processes to be considered.

The proposed approach takes into account the robustness of the controller with respect to these structured uncertainties by using the small-gain theorem.In addition , improved performance is sought through the minimisation of an upper bound to the closed -loop system norm.A Lyapunov - Krasovskii -type functional is used to obtain delay dependent design conditions.The controller design is accomplished by means of a convex optimisation procedure formulated using linear matrix inequalities . In order to illustrate the flexibility of the approach, several examples considering recycle compensation, reduced-order controller design and a practical implementation are addressed. Numerical experiments are provided in each case to highlight the main charecteristics of the proposed design method.