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Unformatted text preview: EE 428 PROBLEM SET 6 DUE: 5 NOV 2007 Reading assignment: Reading assignment: Ch 5, sections 5.1 through 5.7 Problem 25: ( 40 points) Figure 1 shows the block diagram representation of a plant with input control voltage v u ( t ) [V] and output angular displacement θ o ( t ) [deg]. The plant has the transfer function G p ( s ) = Θ o ( s ) V U ( s ) = K A K m K G s ( sτ + 1) deg V and consists of a power amplifier, DC motor, and gearbox connected in cascade. A tachometer converts the angular velocity ω ( t ) [RPM] of the motor shaft into a voltage v ω ( t ) = K T ω ( t ) [V] , where K T = 1 . 5 × 10- 3 [V/RPM] is the tachometer sensitivity. A position sensor consisting of a potentiometer with no physical stops converts the output displacement- 180 ◦ ≤ θ o [ deg ] ≤ 180 ◦ into a voltage v θ o ( t ) = K θ θ o ( t ) [V] , where K θ = 28 . 4 × 10- 3 [V/deg] is the position sensor sensitivity. Using measured input-output data, a control engineer estimates the transfer function from the input control voltage v u ( t ) to the tachometer output voltage v ω ( t ) as V Ω ( s ) V U ( s ) = 1 . 2 . 021 s + 1 V V . The gearbox reduces the output speed of the DC motor by a factor 1 / 70. The gain K G = 6 70 deg V accounts for the gear reduction ratio and maps the motor shaft velocity from units of RPM to degrees per seond. In this problem you will design a feedback control system for regulating the output displacement θ o ( t ) [deg] to a desired value θ r ( t ) [deg]. The desired closed-loop performance specifications are: • A peak overshoot of 5%. • A time-to-peak of 100 ms. • Zero steady-state error for a unit-step input θ r ( t ) = 1 ◦ 1( t ). Figure 1: DC motor system with velocity and displacement sensors. Figure 3 shows a cascade compensation scheme that does not use the tachometer output voltage v ω ( t )....
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This note was uploaded on 07/23/2008 for the course EE 428 taught by Professor Schiano during the Fall '07 term at Penn State.
- Fall '07