Modelling and controller design for a five-link inverted pendulum

The inverted pendulum is a fast-moving, highly nonlinear and unstable system with multiple variables and non-minimum phase that requires effective stabilization controllers. Therefore, studies into inverted pendulum systems theoretically and practically have great significance. The Euler-Lagrange Equation is used to calculate the mathematical model for a five-link inverted pendulum system. Linear Quadratic Gaussian (LQG) and $\mathcal{H}_{\infty}$ are implemented using the developed model, with the Kalman Filter serving as the observer. The closed-loop system are simulated by the Matlab-Simscape platform and the controller are evaluated in relation to the system performance.