Compact Form Linearization and Partial Form Linearization Methods

Using compact form linearization and partial form linearization methods, nonlinear systems can be effectively linearized. Subsequently, PID controllers can be employed for controller design, where the proportional, integral, and derivative gains require systematic tuning through methods like Ziegler-Nichols or optimization algorithms. Beyond PID control, advanced control strategies such as fuzzy logic control (implemented with membership functions and rule bases) and adaptive control (featuring real-time parameter adjustment mechanisms) can be considered to enhance system performance and stability. Further research and optimization of controller parameters using techniques like gradient descent or genetic algorithms can achieve more precise control outcomes. In summary, by linearizing nonlinear systems and integrating appropriate control methods with parameter optimization, efficient and stable controllers can be designed with robust implementation frameworks.