Control (2)(Take class notes)Overshoot solution• Provide velocity feedback: = - = / { - +- +++- +s( Characteristic equation+0• You now have two parameters to adjust the performance: K1and K2 ///= /• K2adds with K1 and B terms to increase damping which is the velocity feedback to anticipate overshootSteady-state error solution (1)• Add an integrator to the feedback• The above control strategy is called PID control• The integral part is to eliminate the steady-state error• The derivative part is to adjust the damping performance as discussed earlier• In the Laplacian domain: = - - −ProportionalDerivative Integral = - −Steady-state error solution (2)• Question: Will any voltage be produced when there is steady-state with zero error?- Yes: the integral term can have a constant output- Problem: the integral term tends to slow down the response and perhaps destabilize the system – why?• Solution: use both proportional and velocity (derivative) feedback control plus a offset voltage: +- ++++- The offset (feedforward) term to the motor• The offset voltage is to generate the torque to balance the load against the gravity Torque generated by Vofffor balancing the load• K1and K2 will work together for a particular motor: R, B, and J• Note that • When n is large, the load inertia and damping can be ignoredFor critical damping• If we want critical damping – fast reaction with no-overshoot:12/ /) + +
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