American Journal of Engineering Research (AJER) 2017 American Journal of Engineering Research (AJER) e-ISSN: 2320-0847 p-ISSN : 2320-0936 Volume-6, Issue-11, pp-44-53 www.ajer.org Research Paper Open Access www.ajer.org Page 44 Optimal Tuning of Dynamic Controller via LQR in a Powered Wheelchair Evandro Martins Araújo Filho 1 , João Viana da Fonseca Neto 2 1,2 (Department of Electrical Engineering, Federal University of Maranhão, São Luís, Brazil) Corresponding Author: Evandro Martins Araújo Filho ABSTRACT: The development of an optimal tuning design for Proportional and Integral (PI) controller, applied to a powered wheelchair, is presented in this paper. The aim is to control the left and right wheels velocities to follow a given reference trajectory by means of a kinematic controller. The optimal tuning is performed through the Linear Quadratic Regulator (LQR) theory, the main idea is to insert the integral action of the PI controller to the system. In this way, the classical mathematical model is developed in state space description to adjust the proportional and integral gains of the PI controller to guarantee an optimal operation of wheelchair. For two case studies, the tuning proposal is evaluated in mathematical model of the wheelchair. The first case is linear trajectory and the second case is a circular trajectory, the evaluation test presented satisfactory results. Keywords: Dynamic Control, LQR, PI Controller, Powered Wheelchair, Optimal tuning. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 25-10-2017 Date of acceptance: 09-11-2017 --------------------------------------------------------------------------------------------------------------------------------------- I. INTRODUCTION A powered wheelchair provides a certain independence to the disabled people, providing more mobility through control usually by joystick. However, there are still many users who have the most varied types of physical disabilities that make it impossible to use this type of control safely [1]. In order to provide more comfort and safety to wheelchair users, it is necessary to implement a more improved motion control system through the dynamic control. To design a controller that meets the demands of the most diverse types of users, a mechanical model of the wheelchair is required. This model is divided into two parts, the first one represents the dynamics and the second the kinematics. These two models become possible a design of the controller based on the simulated response. The main alternative to control system design is Proportional Integrative Derivative (PID) Controller. This controller is commonly used due to their simple structure and operation, which motivates ongoing research efforts to find alternative approaches to the project and new tuning rules to improve control performance in closed loop based on the PID [2]. In this paper is presented the development and implementation of a PI controller tuned through the Linear Quadratic Regulator theory applied to a powered wheelchair with trajectory tracking system. The tuning of the dynamic controller is accomplished by varying the values of the  and  matrices, which gives optimal ܭ ݌ and ܭ  gains. That are associated with the robustness and simplicity of the PI controller. The rest of the paper is organized into five sections. Section II presents the kinematic and dynamic model of mobile robots, which are very similar to that of a powered wheelchair. In Section III, the kinematic controller used is briefly described and the proposed dynamic controller is presented through its mathematical formulation. The computational results are presented in Section IV obtained through the application of the proposed methodology. Finally, the conclusions are presented on the section V. II. POWERED WHEELCHAIR A powered wheelchair is modelled as differential traction mobile robot it has two front and rear wheels. The rear wheels are controllable. Therefore, there is control applicability for this type of system [1] [3]. The acceleration components are inserted for dynamic system representation, so as to result in the variation of wheel rotation. This mechanical energy is a result of the electric power supply to the motors. The