Control System Lab1

UEEA3423 Control Systems Experiment 1 Closed Loop Position Controller & Transient Response of Position Controller

Name: Karthik Suriandran Course: Mechatronic Engineering Student ID: 1100324 Date of Experiment: 1/07/2014 Lecturer: Dr Chew Kuew Wai Title: Closed Loop Position Controller & Transient Response of Position Controller.

Objective:  

To investigate the changes in system response and offset error when the system gain varies. Implement position control using simple proportional controllers and to study the transient response of a position controller.

Abstract: This experiment is done to study the system response when the system gain is increased and decreased. In the first part, a closed loop position controller system is constructed. In theory, when the system gain in reduced, the “deadband” and the offset error increase whereas when the system gain is increased, the offset error is reduces and the system response will increase. As for the second part of the experiment, transient response of a position controller is studied. When the system gain is reduced, the rise time will be longer which makes the system response to be slow and vice versa. When the gain is too high, there will be an overshoot in the system response. When the load to a motor is an inertia type, the transient response slows down.

Introduction: A closed loop position controller is type of control system that automatically changes the output based on the difference between the feedback signal and the input signal. In the first part of the experiment, the positional information from an output potentiometer which is mechanically coupled to a motor is fed back to a control amplifier. Later, the reference position input from the input potentiometer is combined with the feedback signal at the input of the amplifier which drives the motor in proportion to the difference between two signals. The simplified system diagram of the closed loop system used in the experiment is shown in Figure 1 below.

Figure 1

The A1 is an error signal generator, A2 is an error signal amplifier and A3 is driver for the motor M. As the Pi is turned away from Po, the difference between two voltages is the error signal which appears at A1. The error signal is further amplified through A2 and A3 and this

drives the motor in the direction to reduce the error voltage between Pi and Po.When Pi is turned clockwise, Po follows in same direction and continues until the output A1 = 0.

Second part of the experiment is to study the transient response of a position controller. When a step input is fed into the position controller, the loop takes time to react to the applied input. Oscillation also can occur at the output during the transient time depending on the system parameters. The delay is caused by the inertia of the moving parts. When the inertia increases, the delay increases. The transient response can be observed through the oscilloscope when the square wave input is applied as the diagram shown below in Figure 2.

Figure 2

Equipment: 

DC Servo Trainer ED – 4400B

Procedure: Part A: Closed Loop Position Controller

Figure 3 1. The modules are arranged and connected as shown in Figure 3 above which includes coupling of U-158 to U-161. 2. U-152 is set to “a” and U-151 to “10”.U-156 is turned on and U-157 is set to 180 degrees. 3. U-153 is adjusted so that the U-154 output is zero. U-153 is remained untouched after the setting. 4. Now, U-151 is set to “9”.U-157 was turned clockwise or counter-clockwise within +20 degrees from the original 180 degrees so that the U-158 follows the movement. It is seen that U-158 lag U-157. The wires of U-161 motor are switched if U-158 leads U-157. 5. U-157 is turned clockwise from 0 degrees by incrementing every 10 degrees until it reaches 150 degrees. The angle of U-158 is measured at each position of U-157. Measurements of U-157 are repeated by turning counter-clockwise. The offset error angle between U-157 and U-158 at each position are calculated. 6. System gain is increased by setting U-151 to 7, 5, 3, and 1 and the previous step 5 are repeated to take the measurements of offset error angle. 7. Results of Steps 5 and 6 are plotted.

Part B: Transient Response of a Position Controller

Figure 4 1. 2. 3. 4. 5.

The modules are set as shown in Figure 4 above with an oscilloscope. U-151 was set “10” and U-152 was set to “a”. The power of U-156 is turned on. U-153 output was adjusted to be zero. The frequency of U-162 was set to 0.2 Hz. Oscilloscope is adjusted and observed. U-151 was set to “8” and U-158 is observed turning left and right. Oscilloscope is observed and noted. 6. Now, U-151 is set to 6, 4, 2, and 0 in sequence and each impact on the trace at each time is monitored. 7. U-152 is switched to “b” and step 6 is repeated. Resultant response is sketched. Post Problems:

1. Block Diagram

INPUT, U(S)

2. Simplified Block Diagram:

K1

K2

G

OUTPUT, Y(S)

K1K2G + 1

INPUT, U(S)

OUTPUT, Y(S)

3. Transfer Function: T(s) = U(S)/ Y(S) = K1K2G + 1

Results: Part A: Table 1: Offset error angle when the system gain is 1 Input Angle U-157 / (θ°) 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

U-158 (after clockwise rotation) / (θ°) 5 16 26 37 47 57 68 78 88 98 108 118 128 138 148

Offset Error Angle / (θ°) -5 -4 -4 -3 -3 -3 -2 -2 -2 -2 -2 -2 -2 -2 -2

Table 2: Offset error angle when the system gain is 3 Input Angle U-158 Offset Error U-157 (after clockwise Angle / (θ °) rotation) / (θ °) / (θ °) 10 20 30 40 50 60 70

6 15 25 35 45 55 65

-4 -5 -5 -5 -5 -5 -5

U-158 (after counter clockwise rotation) / (θ°) 9 19 30 40 50 60 70 80 90 100 110 120 130 140 150

Offset Error Angle /( θ°) -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0

U-158 (after counter clockwise rotation) / (θ°) 9 19 29 40 49 60 69

Offset Error Angle /( θ °) -1 -1 -1 0 -1 0 0

80 90 100 110 120 130 140 150

75 86 95 105 115 126 135 146

-5 -4 -5 -5 -5 -4 -5 -4

80 90 100 110 120 130 140 150

0 0 0 0 0 0 0 0

Table 3: Offset error angle when the system gain is 5 Input Angle U-158 Offset Error U-158 U-157 (after clockwise Angle (after counter clockwise / (θ °) rotation) / (θ °) / (θ °) rotation) / (θ°) 10 5 -1 10 20 15 -5 17 30 23 -7 28 40 34 -6 38 50 45 -5 48 60 55 -5 58 70 63 -7 68 80 75 -5 79 90 84 -6 88 100 95 -5 99 110 105 -5 109 120 115 -5 119 130 125 -5 129 140 135 -5 138 150 145 -5 149

Offset Error Angle /( θ °) 0 -3 -2 -2 -2 -2 -2 -1 -2 -1 -1 -1 -1 -2 -1

Table 4: Offset error angle when the system gain is 7 Input Angle U-158 Offset Error U-158 U-157 (after clockwise Angle (after counter clockwise / (θ °) rotation) / (θ °) / (θ °) rotation) / (θ°) 10 11 1 15 20 11 -9 16 30 23 -7 25 40 32 -8 35 50 43 -7 46 60 53 -7 56 70 63 -7 68 80 73 -7 75 90 83 -7 86 100 93 -7 96 110 104 -6 107

Offset Error Angle /( θ °) 5 -4 -5 -5 -4 -4 -2 -5 -4 -4 -3

120 130 140 150

114 124 134 144

-6 -6 -6 -6

116 127 137 147

Table 5: Offset error angle when the system gain is 9 Input Angle U-158 Offset Error U-158 U-157 (after clockwise Angle (after counter clockwise / (θ °) rotation) / (θ °) / (θ °) rotation) / (θ°) 10 16 6 21 20 16 -4 21 30 17 -13 23 40 29 -11 30 50 38 -12 43 60 49 -11 50 70 56 -14 62 80 69 -11 70 90 78 -12 82 100 89 -11 94 110 99 -11 101 120 108 -12 113 130 120 -10 120 140 128 -12 133 150 140 -10 141

-4 -3 -3 -3

Offset Error Angle /( θ °) 11 1 -7 -10 -7 -10 -8 -10 -8 -6 -9 -7 -10 -7 -9

Part B: 1. U-152 was set to “a”. U-151 was varied from 8, 6, 4, 2, and 0 and the oscilloscope results are as follows: U-151 = 8

U-151 = 6

U-151 = 4

U-151 = 2

U-151 = 0

2. U-152 was set to “b”. U-151 was varied from 6, 4, 2, and 0 and the oscilloscope results are as follows:

U-151 = 6

U-151 = 4

U-151 = 2

U-151 = 0

3. A flywheel is attached to the high speed shaft of the servo motor. U-152 is set to “a”. U-151 was varied from 6, 4, 2, and 0 and the oscilloscope results are as follows:

U-151 = 6

U-151 = 4

U-151 = 2

U-151 = 0

Discussion: Conclusion: References: