Parameter-optimized Controllers for Stochastic Disturbances

Abstract

The parameter-optimized control algorithms given in chapter 5 can be modified to include stochastic disturbance signals n(k) by using the quadratic performance criterion

$$S_{eu}^2 = \sum\limits_{k = 1}^M {\left[ {{e^2}\left( k \right) + rK_p^2\Delta {u^2}\left( k \right)} \right]} $$

(13.1)

if the disturbance signals are known. When using a process computer, the stochastic noise can first be stored and then used in the optimization of controller parameters. If the disturbance is stationary, and if it has been measured and stored for a sufficiently long time, it can then be assumed that the designed controller is optimal also for future noise and a mathematical noise model is not necessary for parameter optimization.