Hi Anteneh Tadesse Yitbark,

I don't understand.

Hello, yew-chung chalk. My advisor told me the sliding manifold is goes to infinity and we have to bound it. And I want to add fuzzy logic to tune the gain of the sliding mode which is c1,c2&c3. On the simulink I send to you.

Are c1, c2, c3 constant-valued gains?

yes they are,

If c1, c2, c3 are constant-valued gains, then fuzzy logic is unsuitable for this application.

Perhaps the metaheuristic methods in the Global Optimization Toolbox such as Genetic Algorithm, Particle Swarm, and Simulated Annealing are useful for tuning the constant-valued gains.

https://www.mathworks.com/help/gads/index.html

ok, i will check them out, but if it is not constant gain how can i tune them using fuzzy. thanks

If the gains are time-varying, you need to identify certain conditions that produce desired gains c1(x, t), c2(x, t), c3(x, t) at the macro level. These conditions are inscribed in the fuzzy rule base in form of:

If Condition 1a and Condition 2a are met, then c1 = value1, c2 = value2, c3 = value3.

If Condition 1a and Condition 2b are met, then c1 = value4, c2 = value5, c3 = value6.

If Condition 1b and Condition 2a are met, then c1 = value7, c2 = value8, c3 = value9.

If Condition 1b and Condition 2b are met, then c1 = value10, c2 = value11, c3 = value12.

You may have multiple types of conditions, not limited to two types of conditions.

Under this conditions, it is reuiered a expert human who can provide the operations rules and membershio functions. Otherwise, it can be used a datadiven approach to find them