MAE 334 Introduction to Computers and Instrumentation Lab 2 (Week 1,2,3 &4): Motor modeling and position control

Author: Deepak Kumar
Lab Partner: DE SILVA T C J
Date: 4/24/2012 4:02 PM Lab TA: Reza Lab Section: L6 –Monday 6:30-9:00 PM

Integrity Statement:

I understand the importance of ethical behavior in engineering practice and the seriousness of plagiarism. I am pleased to confirm that this work is our own independent effort. All of the data processing and graph preparation is our own. We prepared the written text in this report independently and we did not copy the work of anyone else into our report.

Signature #1: JEEVAN SUPARMANIAM Lab Manual & Title Sheet | | 5% | MATLAB Development | | 10% | Notebook Review | | 10% | Post Lab Oral Presentation | | 25% | Results | | 25% | Discussion of Results | | 15% | Quality | | 10% | Total Score | | 100% |

Objectives
Week 1 * To model DC motor velocity as first and second order systems and simulate with Simulink * To simulate PD closed loop controller using Simulink
Week 2 * To develop an understanding of the basic Quanser Inc., QuaRC Software servo motor software and hardware setup and connections * To quantify the values of K and τ from the experimental data using the MATLAB curve fitting toolbox and from the time series graph * To develop an understanding of how the system responds to different input signals
Week 3 (&4) * To study the transient characteristics of a typical second order system and evaluate model or system responses * To analyze the effects of proportional-, derivative- and integral- control individually and in combination on the closed loop response of motor * To solve a position control problem by calculating the PD controller gains analytically and validate the control by monitoring the motor response for different desired trajectories * To design a PID controller for the actual DC motor using Ziegler-Nichols’ method and compare the performance with that of the PD controller methods (i) WEEK 1
Firstly, the 64-bit MATLAB is launched. Using Simulink, a Simulink model is created based on the figure provided in the lab manual (week 1). The Simulink model has a step, motor transfer function and scope. Under “Solver Options”, the Type is changed to “Fixed stepped”, Solver is changed to “ode4(Runge-Kutta)” and the fixed step size is set to be 0.001. In the “Transfer Fcn” of the Simulink, the numerator coefficient is set to [K] and the denominator coefficient is set to [tau 1]. The motor parameters K and τ are calculated based on the equations (Electrical , Mechanical and Actuator Dynamics) and the nominal values provided. The simulation stop time is set to 2 seconds. The simulation is then started and the corresponding response is seen in the scope. The signals are then plotted. Then a small change is done to the “Transfer Fcn” block and the denominator is changed to [tau 1 0]. | Deepak Kumar
Partner: DE SILVA T C JTA: Reza | Lab Section: L6 –Monday 6:30-9:00 PME-mail: [Company E-mail] |
The corresponding signal is plotted. As final part, a Simulink model for closed loop PD motor control system is made based on the figure provided in the lab manual. In this model, a proportional control and a derivative control have been incorporated. The simulation model is then run for the kp and kd values given in the manual. The corresponding signals are plotted and discussed. (ii) WEEK 2
Firstly, the 64-bit MATLAB is launched. “LabQuarcSetup.m” file, which is a Simulink model, is acquired from the class directory and is then run. To do the DAQ Hardware setup, SRVO2-ET Experiment #1: Modeling [1] Simulink module q_srv02_mdl is opened. A few sub blocks are opened by double-clicking on them. The order is as follows: SRV02-ET Speed -> SRV02-ET -> QuaRC HIL Initialize HIL-1. The parameters are set based on the manual (week 2). The step input source block is opened and the parameters are set based on the manual. On the Spd Src block, the Enc is set to 2. Also, in the Time box, the model execution time is set to 1.5 second. On the w_l(rad/s) Scope, the x-axis limit is set to 1.5 seconds, and then the Simulink module is compiled by clicking on the “build” button. Once the build process is completed, the compiled code is downloaded by clicking on the “connect to target” button; then, the model is run by clicking on the play button. The motor response plots produced in the w_l(rad/s) Scope are then plotted using the MATLAB commands provided in the manual.
To enable accurate estimation of the step input start time (usually around 0.015), the time constant and the final steady state value, the initial part of the plot is zoomed in using the data cursor in the plot window. The time constant, τ and the final steady state value of the angular velocity, y∞ are estimated. The gain of the system, K, is calculated using the following equation:
K= y∞ stepsize.
The estimated results are tabulated. Then, using the curve fitting tool:>> cftool, the time constant is found. The procedure is explained thoroughly in the lab manual. The process is repeated for step values of 0.6, 0.8, 1.0 and 1.2. The results are then recorded and tabulated. As for the modeling the physical system, the Simulink file q_rsrv02_mdl is opened. The signal generator is selected as a source by toggling the manual switch. The amplitude is set to 5, and the frequency is set to 0.02 Hz. The time parameter in the w_l(rad/s) Scope is set to 100 seconds, and the time box in the header of the model window is set to “inf”. The model is built, and then is run. Using the MATLAB commands provided, the signal response is obtained. The process is repeated for other wave types. The corresponding omega responses and the theta responses are plotted. The amplitude and the frequency are altered to get some observations. (iii) WEEK 3 (&4)
Firstly, the 64-bit MATLAB is launched. “setupsrv02pos.m” file is acquired from the class directory and is then run to initialize the parameters. The Simulink model “qsrvo2pos.mdl” is opened. The step size is set to 1. The values of the PID gains are modified in the “setupsrv02pos.m” file in line 112-115, where Kd = 0 and Kp = 50. The model is built and then is run. The corresponding responses are plotted using the MATLAB commands provided. The data displayed on the command window is also recorded. The same process is repeated for other values of the PID gains based on the modes(P, D, I) required. The results are then tabulated. The PD controller is designed based on my person number and lab partner’s person number. From the Mpnewvalue and the Tsnewvalue, the new natural frequency, (ωnnew) and the new damping ratio, ζnew are computed. The Kd and Kp values are computed using the equations provided in the lab manual. The values are then updated, the Simulink is run, and the results are plotted. The values of the PD gains are intuitively changed to improve the transient response. After that, to implement the PI and PID controllers, the values of the PD gains are reset to Kd = 0 and Kp = 50.
As for the motor, the whole process is repeated for modes P, PD, PI and PID. In this case, first the values for the motor are initialized. Then the model is compiled by “building” it, and the complied code is downloaded by clicking on the “connect to target” button. The results are plotted and tabulated.

Results & Interpretation
WEEK 1
A DC motor as first order system is modeled using Simulink. For this model, the values of K and τ are calculated based on the following equations:
Ωl(s)Vm(s)=ηgηmKgKtJeqRms+(BeqRm+ηgηmKtKmKg2)
Ωl(s)Vm(s)=Kτs+1
The computed values are of K=1.760 andτ=0.0275. The corresponding plots for the appropriate order of the step response are shown below.

Figure [ 1 ]: Velocity response of DC motor (Transfer Function = Kτs+1)

Figure 2 :Open loop position response of DC motor (Transfer Function = Kτs2+s)
The PD controller simulation modeled is shown below. The values of the PD gains are changed and the plots are attached in the appendix section of the report. The main purpose of this lab is to adjust the PD gains and observe what makes the signal to converge faster. Larger proportional control gain causes the steady state error to be smaller, causing the signal to converge faster. In this model, it is better to use a high Kp value and a very low Kd value to get the desired output faster.

WEEK 1: PD Controller Simulations

Figure Number | Kp | Kd | Observation | Figure 3 | 10 | -1 | Signal converges | Figure 4 | -1 | -1 | Signal goes to infinity | Figure 5 | -10 | -10 | Signal goes to infinity | Figure 6 | 10 | 0 | Signal converges | Figure 7 | 1000 | 0 | Signal converges | Figure 8 | 0 | 1 | Input voltage goes to infinity | Figure 9 | 10 | 1 | Input voltage goes to infinity | Figure 10 | 1000 | 5 | Signal converges |

WEEK 2
All the data collected for four different values of step inputs are tabulated below. The corresponding tau values and K values can also be found below. The K and tau errors % are estimated. Some of the corresponding omega responses and theta responses can be found in the appendix section.

WEEK 2: Summery of motor response characteristics with 95% confidence intervals if available Experiment Number | 1 | 2 | 3 | 4 | Output Step Size (volts) | 0.6000 | 0.8000 | 1.0000 | 1.2000 | Data Sampling Rate (Hz) | 1000 | 1000 | 1000 | 1000 | Final Steady State Velocity (rad/sec) omega | 1.1000 | 1.1000 | 1.1000 | 1.1000 | Estimated Gain K | 1.8333 | 1.3750 | 1.1000 | 0.9167 | Estimated Time Constant (sec) tau | 0.0250 | 0.0250 | 0.0250 | 0.0250 | Gain from Curve Fit K | 1.9060 | 1.4300 | 1.1440 | 0.9532 | Time Constant from Curve Fit | 0.0360 | 0.0360 | 0.0360 | 0.0360 | Time Constant from the Week One Model | 0.0275 | 0.0275 | 0.0275 | 0.0275 | Estimated/ Fit Time Constant Error % | 3.8125 | 3.8462 | 3.8462 | 3.8327 | Estimated/Fit Gain Error % | 30.5748 | 30.5748 | 30.5748 | 30.5748 |

WEEK 3 &4
The Simulink model is first run without the motor. The Simulink model is run for the modes listed in the table below. The results of the simulations for a closed loop DC Motor system are plotted.
WEEK 3 : Summery of Position Control Experimental Results ( Simulation) CONTROL | CONTROL GAIN | ESIMATED FROM THE PLOT | FROM THE MATLAB CODE | MODE | kp | kd | ki | tr | ts | td | Mp | tp | tr | ts | td | Mp | tp | P | 50.000 | 0.000 | 0.000 | 0.032 | 0.146 | 0.020 | 0.340 | 0.058 | 0.024 | 0.140 | 0.020 | 0.340 | 0.060 | D | 0.000 | 50.000 | 0.000 | N/A | N/A | N/A | N/A | N/A | 0.003 | 2.000 | N/A | 0.000 | 0.200 | I | 0.000 | 0.000 | 50.000 | 0.120 | N/A | 0.130 | 1.400 | 0.400 | 0.900 | 2.000 | 0.130 | 0.000 | 0.200 | PD | 22.000 | 0.152 | 0.000 | 0.050 | 0.240 | 0.034 | 0.085 | 0.100 | 0.050 | 1.130 | 0.034 | 0.085 | 0.100 | PI | 22.000 | 0.000 | 50.000 | 0.040 | 0.120 | 0.090 | 0.240 | 0.100 | 0.050 | 0.220 | 0.030 | 0.250 | 0.090 | PID | 10.000 | 0.100 | 50.000 | 0.070 | 0.140 | 0.050 | 0.240 | 0.200 | 0.080 | 0.080 | 0.050 | 0.250 | 0.190 |

Then we run the model with the actual motor for the modes P, PD, PI and PID. The results of the actual Motor Plant step input response are plotted. The plots can be found in the appendix section. The comparison between plots of the simulation and of the actual motor plant differ slightly. It could have been said that it is due to some external factors such friction, but it is not possible as the motor responses are faster than the simulated responses. This is because the assumed parameters of the motors which are used in the simulated model are not the exact values of the motor. This is the prime cause for why the motor responses are faster than that of the simulated responses.
WEEK 4 : Summery of Position Control Experimental Results ( Motor Model) CONTROL | CONTROL GAIN | ESIMATED FROM THE PLOT | FROM THE MATLAB CODE | MODE | kp | kd | ki | tr | ts | td | Mp | tp | tr | ts | td | Mp | tp | P | 50.000 | 0.000 | 0.000 | 0.050 | 0.120 | 0.050 | 0.140 | 0.100 | 0.060 | 0.180 | 0.050 | 0.150 | 0.110 | PD | 22.000 | 0.152 | 0.000 | 0.070 | 0.100 | 0.050 | 0.040 | 0.140 | 0.060 | 0.200 | 0.050 | 0.040 | 0.127 | PI | 50.000 | 0.000 | 10.000 | 0.060 | 0.140 | 0.050 | 0.140 | 0.120 | 0.060 | 0.190 | 0.050 | 0.140 | 0.100 | PID | 50.000 | 0.020 | 8.000 | 0.060 | 0.140 | 0.050 | 0.130 | 0.120 | 0.060 | 0.180 | 0.050 | 0.140 | 0.100 |

It is also observed that the controller gains affect the values of the rise time, overshoot, settling time and steady state error which ultimately results in the stability of the system. The summary of the effects is found in the table attached below.
Basically, the table below shows the effects of each parameter. The table below has been used as a guideline in estimating the parameters to get a graph that converges faster.

| Deepak Kumar
Partner: DE SILVA T C JTA: Reza | Lab Section: L6 –Monday 6:30-9:00 PME-mail: [Company E-mail] |
REFERENCES
1. Woodward, Scott H. MOTOR MODELING AND POSITION CONTROL LAB. Buffalo : UB, 2012. Lab.
2. Alamdari, Aliakbar AN INTRODUCTION TO SIMULINK. Buffalo : UB, 2012. Lab.

Appendix
WEEK 1

Figure 3 PD controller simulation 1

Figure 4 PD controller simulation 2

Figure 5 PD controller simulation 3

Figure 6 : PD controller simulation 4

Figure 7 : PD controller simulation 5

Figure 8: PD controller simulation 6

Figure 9 : PD controller simulation 7

Figure 10 : PD controller simulation 8

WEEK 2

Figure 11 angular velocity step input motor response and model fit to data

Figure 12 : Angular Velocity response for sine input

Figure 13 : Plot of angular position, teta, for several periods

Figure 14 : Angular Velocity response for square input

Figure 15 : Angular Velocity response for saw tooth input

WEEK 3 (WITHOUT A MOTOR)
MODE P

MODE D

MODE I

MODE PD

MODE PI

MODE PID

WEEK 4 (WITH AN ACTUAL MOTOR)

MODE P

MODE PD

MODE PI

MODE PID

(Sine wave)

(triangle wave)