ece580 lecture 07

ece580 lecture 07 - Sept. 27, 2011 Feedback Control Systems...

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Unformatted text preview: Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 1 Lecture 7 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 2 Announce PS 3 available Due Thursday Password for PS solutions: feedback Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 3 Basic Control System Elements How to select D ( s ) to achieve benefits? Three basic elements Proportional Integral Differential- ( 29 D s ( 29 G s ( 29 Y s ( 29 U s ( 29 R s ( 29 E s ( 29 W s ( 29 o W s ( 29 p U s ( 29 N s (P) (I) (D) PID Controller If no derivative element (PI Controller) Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 4 Proportional element ( 29 ( 29 p u t k e t = ( 29 ( 29 p U s k E s = ( 29 p D s k = Integral element ( 29 ( 29 t I u t k e ds = ( 29 ( 29 I k U s E s s = ( 29 I k D s s = Steady-state response can be zero For signals after exogenous input and before integrator Free integrator Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 5 Exercise Consider the unity feedback system ( 29 D s ( 29 G s ( 29 r t- ( 29 e t ( 29 u t ( 29 y t ( 29 w t ( 29 ( 29 ( 29 1 2 p D s k G s s s = = + Find the closed-loop transfer function from r to y Pick the value of kp that gives a peak overshoot of approximately 10% Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 6 The closed-loop transfer function is ( 29 ( 29 2 p k L s s s = + ( 29 ( 29 ( 29 ( 29 ( 29 2 2 1 2 1 2 p p ry p p k k L s s s T s k L s s s k s s + = = = + + + + + The peak overshoot of a 2nd order system with no zeros is determined by the damping ratio 10% overshoot 0.59 0.6 = ( 29 D s ( 29 G s Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 7 Damping ratio and natural frequency ( 29 2 2 p ry p k T s s s k = + + 2 2 2 n p n k = = 2 2 2 n n s s + + 2 1 2 n p n p k k = = = ( 29 2 1 0.6 2.8 0.6 p k = = Matlab Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 8 Today PI controllers Differential control element Reading FPE 4.3 Sept. 27, 2011 Feedback Control Systems (I) Douglas Looze 9 Basic Control System Elements DC motor control motivation P controller increases speed of response...
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ece580 lecture 07 - Sept. 27, 2011 Feedback Control Systems...

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