The Controller Design Using Local Stability Analysis on a Nonlinear Inverted Pendulum

Abstract

This paper is designed for the purpose of analytic design and numerical simulation of a controller for nonlinear mobile inverted pendulum. It needs to obtain a method to overcome the difficulties in the design problem of controller for nonlinear plant. The method was using local stability analysis of two fixed points in two-dimensional ordinary nonlinear differential equation. The result provides a stable response solution using a special pole placement design, and transient stability is simulated using simulink. The response behavior can be selected according to the desired poles. The results obtained at this work are different from the optimal control problem. Indeed, our results have been summarized in the design method, target response and simulation process.

How A PID Controlling A Nonlinear Plant

“…The response of the system should be simulated by using SIMULINK [8][9][10], to shows various changes in parameter selection on PID, as shown in Figure 5. All blocks in the sub system are arranged according to the formula in the Equation (1) and Equation (4). Subsystem Figure 9 was made to implement an optimal control system, so that at any time the system performance can be regulated through certain damping factors and certain natural frequencies.…”

“…One of output of a nonlinear inverted pendulum model is angle movement, as shown in Figure 1 [1]. These dynamics [2,3] can be elaborated by nonlinear second order differential equation shown with its arrangement as can be seen in Equation (1).…”

“…One of output of a nonlinear inverted pendulum model is angle movement, as shown in Figure 1 [1]. These dynamics [2,3] can be elaborated by nonlinear second order differential equation shown with its arrangement as can be seen in Equation (1). Where 1 is the angle of the pendulum (in radians) from vertical axis, and u is the force applied to the cart (in Newtons).…”