Comparative Analysis of LQR Control Performance between Linear and Discrete Time Nonlinear Inverted Pendulum Models
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Abstract
This paper presents an analysis and performance evaluation of a Linear Quadratic Regulator (LQR) synthesized from a linearized model and applied to stabilize a cart–inverted pendulum system with nonlinear dynamics in a discrete-time framework. The study focuses on investigating the effects of system nonlinearities on control accuracy and robustness through simulation-based comparisons between linear and nonlinear models at initial pendulum angles of 15° and 30°. The results show that at an initial angle of 15°, the responses of both models are closely aligned. In contrast, at 30°, noticeable discrepancies arise due to nonlinear effects, with maximum deviations of approximately 25%, 18%, and 14% observed in cart position, pendulum angle, and cart velocity, respectively, compared to the linear model. Nevertheless, the LQR controller successfully maintains system stability and drives the system toward the equilibrium point. These findings highlight the practical limitations of linearized control design when applied to highly nonlinear systems and suggest future opportunities for advanced data-driven or artificial intelligence-based controllers to further enhance performance, reduce model mismatch, and improve adaptability under complex operating conditions.
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Copyright belongs to Srinakharinwirot University Engineering Journal
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