Chattering performance criteria for multi-objective optimisation gain tuning of sliding mode controllers

Sliding mode control (SMC) is a robust control technique which, however, often shows undesirable chattering phenomena. In the design and gain tuning of SMCs, it is therefore important to try to minimise chattering. When tuning controller gains, there are often conflicting objectives, such as minimising error, minimising control input magnitude, and minimising chattering, that need to be taken into consideration. For nonlinear systems such as quadrotors, optimal gain tuning taking into account multiple conflicting objectives, can be obtained using multi-objective optimisation (MOO) methods. While error and control input performance criteria exist that can be used in MOO gain tuning methods, performance criteria specifically for SMC chattering are required. Therefore, this paper presents chattering performance criteria for SMCs that can be used to minimise chattering when tuning the controller gains. The chattering performance criteria are based on frequency analysis of the control input, making use of the discrete Fourier transform. In this paper, multi-objective particle swarm optimisation (MOPSO) is used for gain tuning of the SMCs, using the developed chattering performance criteria. Simulated and experimental results for the pitch angle control of a quadrotor are used as an example to test the effectiveness of the proposed chattering performance criterion. The results show that the proposed chattering index gives a good measure of chattering. Using the chattering index as one of the objectives for the MOPSO algorithm, gains that minimise chattering and control input, while providing good tracking control, can be selected.