Abstract
A randomized algorithm is suggested for the syntheses of optimal PID controllers for MIMO coupled systems, where the optimality is with respect to the H ∞ -norm, the H 2 -norm and the LQR functional, with possible system-performance specifications defined by regional pole-placement. Other notions of optimality (e.g., mixed H 2 / H ∞ design, controller norm or controller sparsity) can be handled similarly with the suggested algorithm. The suggested method is direct and thus can be applied to continuous-time systems as well as to discrete-time systems with the obvious minor changes. The presented algorithm is a randomized algorithm, which has a proof of convergence (in probability) to a global optimum.
Highlights
Proportional Integral Derivative (PID) controllers are the most widely-used controllers in industry despite of many new results in control theory that have been achieved in recent years
The performance achieved by PID controllers can be significantly improved by using more effective design techniques
We suggest a randomized algorithm for PID optimal controllers
Summary
Proportional Integral Derivative (PID) controllers are the most widely-used controllers in industry despite of many new results in control theory that have been achieved in recent years. In [3] the need for effective methods for the design of PID optimal controllers for MIMO coupled systems that cannot be well approximated by second-order systems, was raised. In [4] the parametrization of all the solutions of the standard H∞ control problem is used to obtain Bilinear Matrix Inequalities (BMI’s) constraints on the PID gains for each frequency. In [5] a method for MIMO coupled systems PID controller design for stable plants (given by transfer function at an appropriate set of frequencies) is represented. The ILMI method needs a good starting point and has no proof of convergence in general Another closely related approach is given in [13] where the 2-Degree of Freedom PID (2-DOF-PID). Y, i.e., the minimal closed convex set that contains X ∪ Y
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call