An algebraic method for designing controllers for multi-input multi-output linear systems via s -domain input-output decoupling

Abstract

The method introduced here is applicable for multi-input multi-output, linear, and time-invariant systems. The state and output equations of the system, which are originally expressed in the t-domain, are first transformed into the s-domain. Then, input-output decoupling is achieved by generating the actual control variables as combinations of virtual control variables in such a way that each output is controlled by only the dedicated one of the virtual control variables. As the next stage, appropriate linear controllers are designed to generate the virtual control variables with feedback, feedforward, and disturbance rejection features. The design method is algebraic and involves the assignment of not only the closed-loop poles but also the type numbers associated with the reference and disturbance inputs. The multivariable transformation filter that converts the virtual control variables into actual ones is formed properly to prevent any possibility of internal instability.