Internal Model Control using the Linear Quadratic Regulator Theory

The Linear Quadratic Regulator theory is applied to the design of Internal Model Control for single-input, single out-put systems. The proposed technique provides an easy and sound alternative to obtain the best stable inverse of the plant model that limits the achievable control quality and yields a stable open-loop controller which is optimal when the model fits the plant exactly. Constraints in the control variable can be handled by a single tuning parameter that is adapted online to yield maximum performance to set-point changes. This study demonstrates that when using open-loop controllers, like IMC, in the presence of constraints, a better performance is obtained if the controller is adjusted to account for the constraints instead of ignoring them.