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Lecture Notes (13)

# Input then what is the output ut ut yt yt 1 0 0 tf

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Unformatted text preview: o a first-order system. Input Then, what is the output? u(t) u(t) y(t) y(t) 1 0 0 TF from motor input voltage to TF motor speed is 1st-oder motor 1stmotor position is 2nd-order motor 2nd(Partial fraction expansion) 5 How to eliminate steady-state error Make a feedback system with a controller having Make an integrator (copy of Laplace transform of a unit step function): Meaning of K and T K : Gain Gain K=1,T=1 Final (steady-state) value Final (steady- 1 0.8 Controller T : Time constant Time 1 Time when response Time rises 63% of final value Indication of speed of Indication response (convergence) Response is faster as T Response becomes smaller. 0 One has to select controller parameters to stabilize the feedback system. Suppose K=T=1, and obtain such parameters! 7 Amplitude u(t) u(t) 6 0.6 0.4 0.2 0 0 1 2 3 Time 4 5 6 8 DC gain for a general system Settling time of 1st-order systems DC gain : Final value of a unit step response DC For first-order systems, DC gain is K. For firstFor a general stable system G, DC gain is G(0). For G, R...
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