Adaptive PSO for optimal LQR tracking control of 2 DoF laboratory helicopter

Abstract

This paper deals with the attitude tracking control problem for a 2 DoF laboratory helicopter using optimal linear quadratic regulator (LQR). As the performance of the LQR controller greatly depends on the weighting matrices (Q and R), it is important to select them optimally. However, normally the weighting matrices are selected based on trial and error approach, which not only makes the controller design tedious but also time consuming. Hence, to address the weighting matrices selection problem of LQR, in this paper we propose an adaptive particle swarm optimization (APSO) method to obtain the elements of Q and R matrices. Moreover, to enhance the convergence speed and precision of the conventional PSO, an adaptive inertia weight factor (AIWF) is introduced in the velocity update equation of PSO. One of the key features of the AIWF is that unlike the standard PSO in which the inertia weight is kept constant throughout the optimization process, the weights are varied adaptively according to the success rate of the particles towards the optimum value. The proposed APSO based LQR control strategy is applied for pitch and yaw axes control of 2 Degrees of Freedom (DoF) laboratory helicopter workstation, which is a highly nonlinear and unstable system. Experimental results substantiate that the weights optimized using APSO, compared to PSO, result in not only reduced tracking error but also improved tracking response with reduced oscillations.