Abstract
An inverted pendulum is a multivariable, unstable, nonlinear system that is used as a yardstick in control engineering laboratories to study, verify and confirm innovative control techniques. To implement a simple control algorithm, achieve upright stabilization and precise tracking control under external disturbances constitutes a serious challenge. Observer-based linear quadratic regulator (LQR) controller and linear matrix inequality (LMI) are proposed for the upright stabilization of the system. Simulation studies are performed using step input magnitude, and the results are analyzed. Time response specifications, integral square error (ISE), integral absolute error (IAE) and mean absolute error (MAE) were employed to investigate the performances of the proposed controllers. Based on the comparative analysis, the upright stabilization of the pendulum was achieved within the shortest possible time with both controllers however, the LMI controller exhibits better performances in both stabilization and robustness. Moreover, the LMI control scheme is effective and simple.
Highlights
Control of an inverted pendulum using various control strategies has become a topic of interest for many years owing to being an under-actuated, unstable, multivariable and non-linear
This paper presents a comparison of observer-based linear quadratic regulator (LQR) and linear matrix inequality (LMI) controllers for stabilization control of an inverted pendulum system
The system is completely stable after applying the observer-based LQR controller as shown in Figure 9, whereby all poles of the system were located in the negative half-plane
Summary
Control of an inverted pendulum using various control strategies has become a topic of interest for many years owing to being an under-actuated, unstable, multivariable and non-linear. A feedback linearization and sliding mode control approach were established to stabilize a class of fourth-order nonlinear systems where design parameters of the sliding surface were modified using the adaptation laws, based on the gradient descent technique [9]. Another approach by [10], stabilized a wheeled inverted pendulum using one accelerometer with a modified mechanical structure. Approximate feedback linearization and sliding mode methods were employed to control a cart-type inverted pendulum, where stability was achieved by using an optimized hybrid algorithm based on the particle swarm optimization and genetic algorithm [11].
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