Internal model control: robust digital controller synthesis for multivariable open-loop stable or unstable processes

Abstract

The two-step internal model control (IMC) procedure is presented for the synthesis of multivariable discrete controllers. This paper adds the following features to the IMC design methodology: (i) extension to open-loop unstable plants; (ii) design of the first-step (no model error) IMC controller so that the L₂-error (sum of squared errors) is minimized for every set-point or disturbance vector in a designer-specified set and their linear combinations; (iii) the second-step (model-plant mismatch) multivariable low-pass filter is designed for robust stability and performance by minimizing a non-conservative robustness measure, the ‘structured singular value’; (iv) the potential problem of intersample rippling is avoided by introducing a modification in the first-step controller and formulating the robust performance objective for the continuous plant output.