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Dynamics Notes

# The open and closed loop systems are both firstorder

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Unformatted text preview: ver drive error to e = 0 Example dx = x+u dt u= p= X ( s) = • • • • Without control (u=0), the system is unstable If Kp > 1, then the closed loop system is stable (pole in RHP). The open and closed loop systems are both first ­order and linear. The input to the closed loop system is xdes(t). Set Kp = 2, x(0) = 0, and consider a step change in xdes. X ( s) = x (t ) = lim x(t ) = t →∞ Steady ­state error! Features of integral control • • • • Can drive the steady ­state error to zero Tends to be destabilizing if KI is too large Integral windup is a problem if error is large for a long time Has potential for slow response (integral takes a long time to change) dx = x+u dt u = p = Closed ­loop system is second order, not first order. Consider case with x(0)=0, Kp = 2, KI = 1, with step change in xdes: • No steady ­state error Features of derivative control • • Fast response Highly sensitive to measurement noise...
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