FACULTY OF ENGINEERING AND APPLIED SCIENCE

ENGR 3350U Control Systems Fall 2013

Report of Lab Number: 4

Section CRN#: ……

Date of Experiment: ……………………

Submitted to:

Course Instructor: Professor E. Esmailzadeh, P.Eng.

Lecturer & Laboratory Coordinator: Cliff Chan, MASc, P.Eng. Laboratory TA: Shivam Shukla

We, the undersigned declare that this assignment is our original work only and has neither been submitted for assessment elsewhere, nor has been given in parts or complete to others to be used.

Name Student ID SignatureOlutope Omole 100457114Brett BullockDean RungeNik Vantfoort

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Table of Content…………………………………………………………………………2

1.0 Abstract………………………………………………………………………………3

2.0 Introduction…………………………………………………………………………..4

3.0 Methods and Materials………………………………………………………………..5

4.0 Experimental Procedure……………………………………………………………....6

5.0 Results and Discussion…………………………………………………………….....7

6.0 Conclusion………………………………………………………………………...….8

7.0 Reference………………………………………………………………………......…9

8.0 Appendices…………………………………………………………………….…….10

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1.0 Abstract

3

2.0 Introduction

4

3.0 Methods and Materials

5

4.0 Experimental Procedure

6

5.0 Results and Discussion

Signal Type Amplitude [rad/s]

Frequency [Hz]

Offset [rad/s]

bsp aw

Square Wave

50 0.4 100 1 0

After setting both the proportional and the integral gains to the recommended values by the Ziegler-Nichols method as Kp = 0.4 Kpc and Ti = 0.8 Tpc then Ki = Kp / Ti or Ki =0.5Kpc / Tpc, the resulting 2% settling time is 0.433.Kp 0.4 Kpc 0.4(0.45) 0.18Ti 0.8 Tpc 0.8(0.1) 0.08Ki Kp / Ti (0.5*0.45)/0.1 2.25

It was observed that initially the current and speed are 0 A and 0 rad/s and the voltage is -3.1 V. After the gains were adjusted and the values of Kp , Ki , bsp and Tf changed to 0.18 V.s/rad, 2.25 V/rad, 1 and 0.01 s, the speed decreased and the voltage increased from -3.1V to 7.6V. There was an increase in the amplitude of the vibrations.

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Set-point Weighting

The values of Kp and Ki were set to 0.23 V.s/rad and 2.3 V/rad respectively and the bsp

value is set to 0 with increasing increments of 0.20 to unity (1) and a disturbance torque was applied manually to system. From the results obtained from the experiment, it was observed that the amplitude gets smaller and the power decreases as the Ki increases.

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As the value of bsp approached 1, the speed value slightly fluctuated between 149 rad/s and 147 rad/s before dropping to a 77 rad/s then to a 150 rad/s. This shows the instability of the speed value while that of the voltage remained constant at 7.6 V. The set-point truly had an effect on the response to command as seen in the plots below.

Response to the Load Disturbance The parameters were set as follows with the gain value kp = 0.10 V.s/rad and bsp = 1.0.Amplitude [rad/s]

Offset [rad/s]

aw

0 100 0 Torque was applied by manually and gently touching the inertial load with the finger. As the proportional gain of the controller increased, the power increased as Kp and the amplitude of the vibrations increased also – as seen below in the plots.

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A controller with the pure integral action was chosen such that k i = 1.0 V/rad and a disturbance was also applied as the integral gain was gradually increased with increments of 0.50 V/rad. The amplitude got smaller and the power decreased as the ki increased.

Simulated Load Disturbances: Disturbance Response with PI control An additional voltage was applied to the motor input, setting the parameters as follows; Amplitude as 0 rad/s, Offset as 0 rad/s and aw as 0.The load disturbance torque Qa created by pressing down and holding/releasing the “User switch”. The gain values were to vary and were set from the value of kp = 0.10 .s/rad with increments of 0.10

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V.s/rad. In this case, the values of the speed, voltage and current remained at 0 but it is seen in the diagram that the disturbance caused little vibrations which moved horizontally to the right of the plot. The amplitude increased slightly also as the K p increased. When Ki was increased, the voltage fluctuated, finally increasing to 1.4 V and the amplitude of the vibrations increased also as Ki = 3.0 V/rad.

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6.0 Conclusion

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7.0 References

13

8.0 Appendices

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