Missile Longitudinal Dynamics Control Design Using Pole Placement and LQR Methods

P.V.R.R. Bhogendra Rao; V.S.N. Murthy Arikapalli; Shiladitya Bhowmick; Ramakalyan Ayyagari

doi:10.14429/dsj.71.16232

P.V.R.R. Bhogendra Rao DRDO-Defence Research and Development Laboratory, Hyderabad - 500 058 https://orcid.org/0000-0003-0454-0816
V.S.N. Murthy Arikapalli DRDO-Defence Research and Development Laboratory, Hyderabad - 500 058 https://orcid.org/0000-0002-1761-7416
Shiladitya Bhowmick Defence Research and Development Laboratory, Hyderabad https://orcid.org/0000-0001-9786-817X
Ramakalyan Ayyagari National Institute of Technology, Tiruchirappalli - 620 015 https://orcid.org/0000-0001-7147-1086

DOI: https://doi.org/10.14429/dsj.71.16232

Keywords: Optimal control;, Longitudinal flight dynamics;, Full-state feedback systems;, Pole placement;, Linear quadratic regulator

Abstract

In high-maneuvering missile systems, with severe restrictions on actuator energy requirements, it is desirable to achieve the required performance with least actuation effort. Linear Quadratic Regulator (LQR) has been in literature for long and has proven it’s mettle as an optimal controller in many benign aerospace applications and industrial applications where the response times of the plant, in most cases, are seen to be greater than 10 seconds. It can be observed in the literature that LQR control methodology has not been explored enough in the tactical missile applications where requirement of very fast airframe response times are desired, typically of the order of milliseconds. In the present research, the applicability of LQR method for one such agile missile control has been critically explored. In the present research work, longitudinal dynamic model of an agile missile flying at high angle of attack regime has been established and an optimal LQR control solution has been proposed to bring out the required performance demanding least control actuator energy. A novel scheme has been presented to further optimise the control effort, which is essential in this class of missile systems with space and energy constraints, by iteratively computing optimal magnitude state weighing matrix Q and control cost matrix R. Pole placement design techniques, though extensively used in aerospace industry because of ease of implementation and proven results, do not address optimality of the system performance. Hence, a comparative study has been carried out to verify the results of LQR against pole placement technique based controller. The efficacy of LQR based controller over pole placement design techniques is successfully established with minimum control energy requirement in this paper. Futuristic high maneuvering, agile missile control design with severe space and energy constraints stand to benefit incorporating the controller design scheme proposed in this paper.