2 - feedback2 filled

2 - feedback2 filled - ME 575 Handouts Disk Drive Head...

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Unformatted text preview: ME 575 Handouts Disk Drive Head Positioning Objective: to precisely locate the head over the disk Options: 1) Open-loop control (without feedback) 2) Closed-loop control (with feedback) School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 1 Open-Loop Control Desired Track Position Controller Motor Voltage C Motor G School of Mechanical Engineering Purdue University Actual Head Position ME575 Session 2 - Feedback 2 1 ME 575 Handouts Open-Loop Control (with Disturbance) Desired Track Position Controller Voltage Disturbance Motor Voltage ++ C Motor Actual Head Position G School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 3 Introduce Feedback R(s) Controller + − C D(s) ++ Plant Y(s) G + + N(s) R(s): reference input signal for desired action D(s): disturbance signal acting on plant N(s): noise signal corrupting the measurement School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 4 2 ME 575 Handouts Closed-Loop Feedback Control R(s) Controller + − C D(s) ++ Plant G Y(s) + + N(s) Y (s) = CG G CG R (s) + D (s) − N(s) 1 + CG 1 + CG 1 + CG School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 5 Closed-Loop Feedback Control • Every transfer function between any one input and one output has the same denominator but different numerators. • The controller C affects inputs R and N in a similar way, but affects input D differently. School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 6 3 ME 575 Handouts Closed-Loop Control Requirements • YR → R ⇒ YR ( s ) = CG R (s) 1 + CG • YD → 0 ⇒ YD ( s ) = G D (s) 1 + CG • YN → 0 ⇒ YN ( s ) = − CG N(s) 1 + CG School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 7 Summary of Feedback Control • The use of feedback provides a mechanism to compensate for disturbances. • High-gain feedback essentially approximates plant inversion (the essence of control). • High-gain proportional control provides good reference tracking and disturbance rejection, but aggravates noise rejection. • How can we reconcile this apparent contradiction? School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 8 4 ME 575 Handouts Frequency Domain Design Assume the reference trajectory is primarily specified at low frequencies and the noise is primarily at high frequencies. Phase (deg); Magnitude (dB) 50 0 -50 -100 -150 -90 -135 -180 -225 -270 -2 10 10 -1 0 10 Frequency (rad/sec) 10 1 10 School of Mechanical Engineering Purdue University 2 ME575 Session 2 - Feedback 9 What about non-unity feedback? R(s) Pre-filter GR Controller + − C D(s) ++ Sensor GS School of Mechanical Engineering Purdue University Plant G Y(s) + + N(s) ME575 Session 2 - Feedback 10 5 ME 575 Handouts Non-unity feedback R(s) Pre-filter GR GS Controller + CGS − D(s) ++ Plant G Y(s) + + N(s) Y (s) = HC′G G C′G R (s) + D (s) − N(s) 1 + C′G 1 + C′G 1 + C′G School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 11 Combine Feedback with Feedforward GF R(s) D(s) C + ++ + Plant + − G Y(s) + + N(s) School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 12 6 ME 575 Handouts Disturbance Feedforward D(s) GD R(s) Controller ++ + − C Plant ++ G Y(s) + + N(s) School of Mechanical Engineering Purdue University ME575 Session 2 - Feedback 13 7 ...
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