i was using the sliding mode control for position control of
ultrasonic motor.
actually the motor operation is rather simple. It has a piezo
material, that is sinusoidally excited, the vibration generated is
transmitted to a moving stage through a spacer. The motion equation is
M d^2(x)/dt^2+ Friction=Kf

***Vc where M is the mass of the moving stage and x is the position, Frixtion is frictional force , Kf is the force constant, and Vc is the control voltage. The control voltage is a dc voltage given to the power electronics driver which generates a sine voltage at fixed frequency but its magnitude proportional to the Vc. I use the sliding surface as below S=lamda***e+de/dt where e si the tracking error e=xd-x; when i use this way the equivalent control obtained from the condition ds/dt=0 is equivalent=M/kf(lamda*de/dt+d^2(xd)/dt^2) when i use this , the de/dt part creates the problem. if i keep lamda small, this rsults in S to change sign so rapidly as de/dt is doing so, results in control signal being changed sign rapidly..thus system screams to die.. if i keep it high so as to supress the effect of de/dt in S , the effect comes in equivalent control, I am just lost how to solve this problem..and its been a long time i am trying it out...can anyone suggest me how to get rid of this problem... jenish