Simple Model-free Control Research Articles

Direct adaptive model-free control of a class of uncertain nonlinear systems using Legendre polynomials

In this paper, a simple model-free controller for a class of uncertain nonlinear systems is presented using Legendre polynomials. According to the orthogonal functions theorem, Legendre polynomials are universal approximators. From this point of view, they are similar to fuzzy systems and can be used as a controller to approximate the ideal control law. Legendre coefficients are estimated online using the adaptation rule obtained from stability analysis. In comparison with fuzzy systems and neural networks, Legendre polynomials are simpler and less computational. Moreover, there are very few tuning parameters in Legendre polynomials. The case studies are an inverted pendulum and an articulated robot manipulator. Simulation results verify the effectiveness of the proposed controller and its robustness against large uncertainties. Comparisons with model-free controller using extended state observer and adaptive fuzzy systems show the superiority of proposed controller in disturbance rejection.

Direct Adaptive Function Approximation Techniques Based Control of Robot Manipulators

In this paper, a simple model-free controller for electrically driven robot manipulators is presented using function approximation techniques (FAT) such as Legendre polynomials (LP) and Fourier series (FS). According to the orthogonal functions theorem, LP and FS can approximate nonlinear functions with an arbitrary small approximation error. From this point of view, they are similar to fuzzy systems and can be used as controller to approximate the ideal control law. In comparison with fuzzy systems and neural networks, LP and FS are simpler and less computational. Moreover, there are very few tuning parameters in LP and FS. Consequently, the proposed controller is less computational in comparison with fuzzy and neural controllers. The case study is an articulated robot manipulator driven by permanent magnet direct current (DC) motors. Simulation results verify the effectiveness of the proposed control approach and its superiority over neuro-fuzzy controllers.

Linear adaptive control of a class of SISO nonaffine nonlinear systems

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.

Simple Model-Free Controller for the Stabilization of Planetary Inverted Pendulum

A simple model-free controller is presented for solving the nonlinear dynamic control problems. As an example of the problem, a planetary gear-type inverted pendulum (PIP) is discussed. To control the inherently unstable system which requires real-time control responses, the design of a smart and simple controller is made necessary. The model-free controller proposed includes a swing-up controller part and a stabilization controller part; neither controller has any information about the PIP. Since the input/output scaling parameters of the fuzzy controller are highly sensitive, we use genetic algorithm (GA) to obtain the optimal control parameters. The experimental results show the effectiveness and robustness of the present controller.