Abstract
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.
Highlights
Sliding mode controllers (SMC) belong to the class of controllers, which are robust and immune to parametric uncertainties of the model
The design of SMC control constitutes two phases; design of a stable sliding manifold that characterizes the system’s dynamics in reduced dimensional form; design of a discontinuous control law that switches across the manifold in its neighborhood while maintaining the global reachability of sliding manifold [1]
We propose a solution to this problem which is summarized as follows: 1) A numerical approach is proposed to solve the SMC design problem for complex nonlinear models with the aim of making the SMC design realizable without performing complex analytical computations
Summary
Sliding mode controllers (SMC) belong to the class of controllers, which are robust and immune to parametric uncertainties of the model. This is because the analytical formulation of SMC requires lengthy algebraic computations, which cannot be carried out for complex models, which is further aggravated by increasing the complexity of the manifolds Another branch of SMCs is the terminal sliding mode, which tackles the shortcoming of asymptotic convergence of regular SMCs, by bringing error trajectories to manifold in a finite and shorter time. We propose a solution to this problem which is summarized as follows: 1) A numerical approach is proposed to solve the SMC design problem for complex nonlinear models with the aim of making the SMC design realizable without performing complex analytical computations.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
