A fast algorithm for reduced-order modeling

A PID type algorithm called Q-PID was developed to improve online quality control of continuous processes. It has adjustable parameters to improve the controlled variable response or to decrease the manipulated variable movements, hence decrease the cost of control. Q-PTD has PTD type terms, a lead/lag term and dead time compensation. All previously published work using this algorithm considered continuous systems. Discrete implementation must be analyzed so that it can be used practically. This paper presents a sound development and simulation of the three possible dead time implementation schemes, Smith predictor, analytical predictor, and generalized analytical predictor that could be used for discrete implementation. It was discovered that either the Smith predictor or analytical predictor techniques could be used in the Q-PID with satisfactory results. The generalized analytical predictor results in drastic cost increases and instability in the presence of modeling error. The Smith predictor is the suggested method as it performs the best in the presence of modeling error and is simple and easy to implement.