Model Order Reduction and Linear Quadratic Regulator Controller Design on A Large Scale Linear Time Invariant System

The main objective of this paper, aims to apply model order reduction on a large scale system and design a Linear Quadratic Regulator (LQR) based controller, to analyse the performance indices, in the time and frequency domains. Control aspects of large scale systems (models with very high order) are a major concern, in the field of control systems. The order of the designed controller must be close to the order of the large scale system, or even more in most cases. As the order of the controller increases the control aspects of the system, it becomes even more complex. Evidently, there are many model order reduction techniques, that reduce the order of the higher order system, without losing the predominant characteristics. A linear quadratic regulator based design is an optimization tool, to derive an optimal controller by minimizing the cost function, based on the two weighting matrices Q and R, which weigh the state vector and the system input, respectively. The step, impulse and the frequency responses of the system with LQR controller are simulated in MatLab. In this paper, a single-input-single-output system (SISO) is considered, nevertheless due to the compatibility of LQR controller, with the state space equations, this study may be extended to multi-inputmulti-output (MIMO) systems, provided the model order reduction techniques are chosen appropriately.