Control Theory: World Heavyweight Championship fight: Sliding Mode Control vs Classic Linear u=Kx

What are the advantages of Sliding Mode Control over PID control? Originally asked on Quora.

Answer by Egor Polilov, Lead Programmer at NTR Lab, on Quora:

In control theory there are systems with a special type of motion, that are sliding modes, which have a high robustness to the additive interferences as well as provide the reduction of the system in the sliding mode and dynamics, which is no worse than one specified in the conditions of parametric uncertainty. The problem of construction of control systems with static and dynamic characteristics closed to the optimal ones according to the set criteria of effectiveness becomes urgent in the conditions of incompleteness of the initial information about the properties of the control object and limited access to the measuring information about its state, which are typical for many technical applications. Motive and search for control laws in the mentioned class of systems are obvious.


In sliding mode closed loop with µ→∞

Control law uy(t) in every quantum of time t generate antiobject!

So, output dynamic is not depend on any variations of object parameters

We have ideal tracking xn(t)=xn*(t), in every quantum of time t



Fig. 1. Ideal tracking problem




Fig. 2. Phase variables xn(t)=xn*(t), all vector x(t) and control law u(t)

Excerpted from the original article [in Russian] by E.V. Polilov,  On The Location Of The Sliding Hyperpsurface Of Relay-Type Modal Systems / 12th International Scientific-Technical Conference on Electromechanics and Robotics “Zavalishin’s Readings” – 2017, Saint Petersburg, Russia.

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Control theory in control systems engineering deals with the control of continuously operating dynamical systems in engineered processes and machines. The objective is to develop a control model for controlling such systems using a control action in an optimum manner without delay or overshoot and ensuring control stability. (Wikipedia)

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