Design of sliding mode control for complex nonlinear models: A numerical approach

In this work, a numerical approach of formulating Sliding Model Control (SMC) is proposed to deal with complex nonlinear models of certain physical systems. Analytical formulation of SMC for such models is not possible as SMCs require algebraic manipulation of system equations, which is not achievable when the system model has strong nonlinearities. For such models, it is proposed to solve the SMC design using a numerical method that deals with numerical values instead of variables or functions in the equations. Mostly, SMC control law is dependent on the bounds of variables that are present in the mathematical expression of time derivatives of the sliding variable. To compute these bounds, a numerical approach is carried out using uncertainty bounds of the system's parameters. Also, a numerical approach is used to compute time derivatives of nonlinear functions that are required in the formulation of SMC. Various forms of SMCs are investigated in this respect, including the basic first-order SMC and a second-order SMC. The proposed framework is generalized as well, making it compatible with a wide range of nonlinear models whose algebraic manipulation is not possible. A prototype example of a nonlinear model of a boiler is used as a proof-of-concept. The simulation results are promising and prove the efficacy of the proposed approach.