I tried to simulate a maglev system with continuous time sliding mode but my simulation is showing error (there is a singularity at one of the integrators). I am attaching the modelling and derivation of the control law here. Please check and tell me what is wrong if any.
The same system is modelled using matlab.
Sliding mode control of a magnetic levitation system
DOI: 10.1155/S1024123X04310033
With Matlab :
https://www.mathworks.com/matlabcentral/fileexchange/52429-example-on-sliding-mode-control
Have a look at :: https://au.mathworks.com/matlabcentral/fileexchange/52429-example-on-sliding-mode-controlArticle Control of MagLev System Using Supertwisting and Integral Ba...
Article Design and Implementation of a Magnetic Levitation System Co...
Sliding mode control of a magnetic levitation system
DOI: 10.1155/S1024123X04310033
With Matlab :
https://www.mathworks.com/matlabcentral/fileexchange/52429-example-on-sliding-mode-control
What's your solver? MATLAB has a suite of good solvers, but they are typically not designed to handle discontinuous right-hand side. Most of MATLAB's methods are variable step-size with the step size controlled by an error estimate, and discontinuities can screw up the error estimator, resulting in the method attempting extremely small steps before giving up the effort. Chattering (see previous answer's link) can be an important issue.
I have done in simulink. I will shortly put the simulink model here. It inherently uses integrators and I have not made any changes to the default ode solver available with simulink
Dear Patra,
As sigma becomes zero as expected, the control force need to approach a balancing value in the range [-1,1] when sigma is zero. But the signum function in Matlab is exactly zero at sigma equals zero, so the result is an averaging via infinitely fine switchings. Either use a fixed step solver if You insist to use sign function, try the boundary layer approach in Sliding mode control or revert to differential inclusions and exact regularization.
Yes, the Kerim is right... furthermore, the "correct" value of the signum function at the discontinuity depends on the values of the right-hand side nearby. So the "correct" signum function depends on the problem. I have a paper giving a general algorithm for handling this in "A high accuracy method for solving ODEs with discontinuous right-hand side" Numer. Math. vol. 58 (1990), no. 3, pp. 299–328. Alternatively, use a smoothing approach (I used this for doing optimal control), as described in "Optimal control of systems with discontinuous differential equations" Numer. Math. 114 (2010), no. 4, 653–695 (with Mihai Anitescu).
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