Abstract
Modeling physical systems usually results in complex high-order dynamic models. It is often desirable to approximate these models by simpler models with reduced order. This study deals with the design of discrete time linear system using a balanced approach reduced order model. The reduced order model retains the desired state variable which contains a significant contribution. A PID controller is designed for the reduced second order model to meet the desired performance specifications by using pole-zero cancellation method. The stabilization of linear discrete time system is achieved by selection of parameters of the PID controller. A numerical example is given to illustrate the design method.
Highlights
Mathematical models of control systems, derived from theoretical considerations, are practically complex and of high order
This study proposes the balanced approach reduced order memory less state space linear discrete time system
The essential part of the state variables of the system is used for the reduction of discrete time systems to obtain stable low order models
Summary
Mathematical models of control systems, derived from theoretical considerations, are practically complex and of high order. Such systems are difficult to be analyzed and the design of controller becomes too difficult. This study describes the reduced order model for a given discrete time linear system keeping only an essential state of the given plant [5,6,7]. The tuned controller is attached with the original higher order system and the closed loop response is observed for stabilization process. Balanced approach reduced order model: Consider a linear discrete time system described by the following equation x(k +1) = Ax(k) + Bu(k).
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