Course Design for Modern Control Theory

Modern control theory course designs frequently utilize the double inverted pendulum as a research subject due to its nonlinear, strongly coupled, and multivariable characteristics, making it an ideal platform for demonstrating control system design methodologies. System Modeling The foundation of double inverted pendulum design lies in dynamic modeling, typically achieved using Lagrangian equations to establish mathematical models. System states include pendulum angles, angular velocities, cart displacement, and velocities. Through linearization techniques, nonlinear models can be transformed into state-space equations, facilitating subsequent controller design. In code implementation, this involves defining state matrices (A, B, C, D) and handling Jacobian matrices for linearization. Controller Design Modern control theory offers various controller design methods including state feedback control, LQR (Linear Quadratic Regulator), and pole placement. The LQR method optimizes control performance by tuning weight matrices Q and R, enabling rapid system stabilization with low energy consumption. Implementation requires solving the Algebraic Riccati Equation using functions like lqr() in MATLAB or control.lqr() in Python. Simulation Verification Simulations using MATLAB/Simulink or Python validate controller effectiveness. By adjusting parameters, engineers observe dynamic responses including stabilization time and overshoot indicators. Simulation blocks typically include state-space models, controller subsystems, and scopes for visualizing response curves. Code implementation involves ODE solvers for numerical integration and real-time plotting libraries. Source Code Implementation Practical code implementation may include state observer design (e.g., Kalman filtering) and real-time control algorithms. Code structure should prioritize clarity for debugging and optimization, ensuring stable operation on hardware platforms like STM32. Key functions typically involve sensor data acquisition, state estimation algorithms, and PWM signal generation for motor control. Extension Considerations Further exploration may include robust control or adaptive control applications for inverted pendulums to address parameter uncertainties and external disturbances, enhancing system anti-interference capabilities. This involves implementing disturbance observers and online parameter adaptation algorithms in the control loop.