Genetic algorithm-based multi-objective design of optimal discrete sliding mode approach for trajectory tracking of nonlinear systems

Abstract

In this paper, a novel multi-objective design of optimal control for robotic manipulators is considered. Generally, robots are known by their highly nonlinearities, unmodeled dynamics, and uncertainties. In order to design an optimal control law, based on the linear quadratic regulator, the robotic system is described as a linear time varying model. The compensation of both disturbances and uncertainties is ensured by the integral sliding mode control. The problem of deciding the optimal configuration of the linear quadratic regulator controller is considered as an optimization problem, which can be solved by the application of genetic algorithm. The main contribution of this paper is to consider a multi-objective optimization problem, which aims to minimize not only the chattering phenomenon but also other control performances including the rise time, the settling-time, the steady-state error and the overshoot. For that, a novel dynamically aggregated objective function is proposed. As a result, a set of nondominated optimal solutions are provided to the designer and then he selects the most preferable alternative. To demonstrate the efficacy and to show complete performance of the new controller, two nonlinear systems are treated in this paper: firstly, a selective compliance assembly robot arm robot is considered. The results show that the manipulator tracing performance is considerably improved with the proposed control scheme. Secondly, the proposed genetic algorithm-based linear quadratic regulator control strategy is applied for pitch and yaw axes control of two-degrees-of-freedom laboratory helicopter workstation, which is a highly nonlinear and unstable system. Experimental results substantiate that the weights optimized using genetic algorithm, result in not only reduced tracking error but also improved tracking response with reduced oscillations.