Investigations on Adaptive Control Schemes to Dynamical Systems

Abstract

newlineThis thesis presents an in-depth investigation into adaptive control strategies applied to dynamical systems, with a focus on two representative systems: the Two-Tank Coupled System (TTCS) and the Inverted Pendulum System (IPS). The study begins by examining the impact of adaptation gain and reference model selection on both first and second-order systems, laying the groundwork for subsequent research. After that, conventional MIT (Massachusetts Institute of Technology), Lyapunov and fractional order MIT(FOMIT) rule-based Model Reference Adaptive Controllers (MRAC) are designed and evaluated for the two-tank coupled system. Subsequently,the modifications in MRAC with PD (Proportional Derivative) and PID (Proportional Integral Derivative) controllers explored to enhance the performance. Transitioning to the inverted pendulum system, conventional MIT,fractional order MIT and modified rule-based MRAC schemes are developed to tackle the inherent instability of the Hinged Inverted Pendulum System. At the end of this thesis, a range of control methodologies including PID, PID with LQR (Linear Quadratic Regulator), Model Predictive Control (MPC), and Adaptive Model Predictive Control (AMPC) are implemented and compared for an Inverted Pendulum Cart System (IPCS). This comprehensive investigation offers valuable insights and methodologies personalized to the complexities of dynamical systems, contributing to the advancement of adaptive control strategies. newlineAn adaptive control law encompasses a regulating control rule compensating for system dynamics variations by adjusting the controller characteristics to maintain the overall system performance. Recently some techniques have been developed based on fundamental aspects of the adaptability of living organisms. The adaptive control method is a technique that measures the dynamic characteristics of the plant automatically and continuously to make a comparison with its required output. It utilizes the difference between plant output and reference output to commut