IJCAS

This paper focuses on enhancing the design of control systems for nonlinear missile models using the feedback linearization (FL) technique. First, the missile model is transformed by employing FL into a quasilinearized fourth order model, permitting the design of well-known linear state feedback control strategies. Several challenges encountered in this process are discussed and the most practical transformation is chosen to arrive at the implementation of the quasi-linearized model in the inner loop around the plant. Secondly, for the outer loop, an optimal control policy of the form u = Kx is devised using the standard linear quadratic regulator (LQR) framework, wherein it is noticed that the choice of the weighting matrices Q (positive semi-definite) and R (positive definite) is of paramount importance in obtaining the state feedback matrix K. Here an attempt is made to place all the four poles at the right locations via the Q and R matrices. This is in contrast to the popular design of considering only a pair of dominant poles and ignoring the effects of the other two poles. The state feedback control u = Kx in the outer loop is converted to a nonlinear control in the inner loop via the transformations employed in FL. Thus, the nonlinear plant remains intact. Next, to tackle the well-known difficult task of arriving at the right set of Q and R matrices, an innovative iterative procedure is proposed to quickly converge to suitable matrices. For the fourth order system, for comparison purposes, the standard state feedback (SSF) controller is also designed. Lastly, the performance of the nonlinear control system designed is compared to that of the linearized missile model controlled using classical techniques, as is mostly found in the literature. The effectiveness and advantages of employing FL techniques are demonstrated through extensive analysis and simulation studies, highlighting the superiority and ease of design of the proposed LQR controller.

Keywords: Feedback linearization (FL), linear quadratic regulator (LQR) control, nonlinear controller, nonlinear missile dynamics, standard state feedback (SSF) control.