Abstract
The optimum feedforward control for a system with a measurable disturbance input is discussed.
Suppose that the optimum state feedback is already synthesized using the linear regulator technique for the system with augmented state variables by adding integrators. In this case, the value of the performance index is given by the quadratic form of the initial value of the state. Let the final value of the augmented state subjected to a step disturbance be x∞. By changing the origin of the state into x∞, the response of the system to the step disturbance is transformed to the response of the system with the initial state -x∞. Then the value of the performance index is given by the known quadratic form of x∞. As x∞ changes with the change of the feedforward, the optimum feedforward can be synthesized to minimize the value of the performance index.
As an example, the synthesis procedure is checked to be valid by the simulation for the control of a drum-type boiler for the case in which the step change of the output steam flow takes place.
The feedforward matrix proposed here is proved to become identical with that of Davison when the weights in the performance index to the added components of the state in the augmentation become zero.
