Stabilization of the cart-inverted-pendulum system using trivial state-feedback to output-feedback control conversion

Abstract

A new linear observer-free output-feedback controller with five adjustable parameters is proposed to stabilize the cart-inverted-pendulum system (CIP) at the unstable equilibrium point. The controller architecture is deduced from a trivial conversion of the linear state-feedback controller that is obtained using a two-step method. First, based on a set of cart change variables, a slightly modified state-feedback controller is developed. Then, the output-feedback controller is obtained through the judicious combination of the cart step reference input internal model and a convenient open-loop state estimator with the above modified state-feedback controller. The local stability of the output-based control system is conducted using the signature formulas method to get simplified conditions. A partial single parameter tuning method and optimal global single parameter tuning method are proposed for adjusting the controller gains to maximize a new efficiency-based objective function. Numerical simulations are first conducted to reveal the simplicity of output-feedback controller design using the partial tuning method, where the state-feedback gains are assumed to be known. Then, an optimal output-feedback controller is designed using the global tuning method. The proposed output-feedback controller is equivalent in terms of performance efficiency to the best five-parameter output-feedback two PID controller.

Keywords

• Cart-inverted-pendulum (CIP) system
• static state-feedback control
• dynamic output-feedback control
• signature formulas stability analysis
• output-feedback two PID controller