New techniques for implementing linear quadratic methods with aerospace and other industrial control applications

The optimal control design for the linear quadratic regulator (LQR) and linear quadratic tracking (LQT) is well known. However, techniques have not been developed that allow the general solution of the LQR and LQT problems to various plants for unsteady-state conditions. This paper revisits these methods and develops MATLAB-based algorithms based on analytical solutions of the matrix Riccati differential equations arising in LQR and LQT methods. It provides an effective control technique for aerospace and other industrial control applications with time-varying set points. To demonstrate, simulations on the use of these techniques are illustrated for two typical applications arising in aerospace and heating, ventilation and air-conditioning (HVAC). It is believed that the implementation techniques developed in this paper serve as an effective tool for optimal design of a variety of problems in industry.