A Comparative Study of LQR, FLQR, SMC, and STSMC for Self Balance Control of a Two-Wheel Electric Wheelchai

Abstract

In today's world, millions of people are physically disabled and have difficulty moving from one place to another due to disease, accident, and age. A wheelchair is an important device, and it is sometimes the only way for those people to become mobile. A two-wheel wheelchair is less expensive than a three-wheel wheelchair and has better mobility and manoeuvrability than a conventional four-wheel wheelchair. However, this two-wheel wheelchair system is highly nonlinear and unstable, necessitating the use of an active controller. The main aim of the work is to develop an effective controller to balance a two wheel wheelchair and perform a comparative study between optimal and robust controllers. In this thesis, linear quadratic regulator, fuzzy linear quadratic regulator, sliding mode controller, and super twisting sliding mode controllers were designed, and their performances are compared and evaluated. First, the SIMO nonlinear system dynamics are modelled using Euler-Lagrange equations based on a double inverted pendulum to account for the system's upper body while also expanding the vehicle's workspace and increasing its flexibility. Nonlinearity obviously makes system modelling and control much more complicated. So the Taylor Series expansion was employed to linearize the nonlinear system. Then controllers are designed based on the linearized model to obtain a fast response. To test the effectiveness of the proposed control methods, the controllers were implemented and simulated using MATLAB/Simulink. The response shows that link 1 has a settling time of 1.208sec, 1.485sec, 2.319sec, and 2.895sec with STSMC, SMC, FLQR, and LQR, respectively. Link 2 has a settling time of 1.408sec, 1.631sec, 2.589sec, and 2.947sec with STSMC, SMC, FLQR, and LQR, respectively. And also, the two-wheeled wheelchair with the STSMC controller has attained a 2.72%, 4.8%, and 98.3% fall in distance travelled in comparison with the SMC, FLQR, and LQR controllers, respectively. These transient response performances show that the STSMC outperformed the other proposed controllers.