DC Motor Control Trainer - Control of Mechanical Systems | ME 439, Study notes of Mechanical Engineering

Download DC Motor Control Trainer - Control of Mechanical Systems | ME 439 and more Study notes Mechanical Engineering in PDF only on Docsity! Quanser NI-ELVIS Trainer (QNET) Series: QNET Experiment #01: DC Motor Speed Control DC Motor Control Trainer (DCMCT) Student Manual DCMCT Speed Control Laboratory Manual Table of Contents 1. Laboratory Objectives.........................................................................................................1 2. References...........................................................................................................................1 3. DCMCT Plant Presentation.................................................................................................1 3.1. Component Nomenclature...........................................................................................1 3.2. DCMCT Plant Description..........................................................................................2 4. Pre-Lab Assignment............................................................................................................2 4.1. Exercise: Open-loop Modeling...................................................................................3 5. In-Lab Session.....................................................................................................................5 5.1. System Hardware Configuration..................................................................................5 5.2. Experimental Procedure...............................................................................................5 Revision: 01 Page: i DCMCT Speed Control Laboratory Manual = − − ( )Vm t Rm ( )Im t ( )Eemf t 0 [1] and = ( )Eemf t Km ( )ωm t . [2] The mechanical equations describing the torque of the motor are = ( )Tm t Jeq ⎛ ⎝ ⎜⎜ ⎞ ⎠ ⎟⎟d d t ( )ωm t [3] and = ( )Tm t Kt ( )Im t , [4] where Tm, Jeq, ωm, Kt, Km, and Im are described in Table 2. Symbol Description Unit Vm Motor terminal voltage V Rm Motor terminal resistance Ω Im Motor armature current A Kt Motor torque constant N.m/A Km Motor back-electromotive force constant. V/(rad/s) ωm Motor shaft angular velocity rad/s Tm Torque produced by the motor N.m Jeq Motor armature moment of inertia and load moment of inertia kg.m2 Table 2 DC Motor Model Parameters 4.1. Exercise: Open-loop Modeling Derive the open-loop transfer function, ωm(s)/Vm(s), representing the DC motor speed using equations [1], [2], [3], and [4]. Revision: 01 Page: 3 DCMCT Speed Control Laboratory Manual Solution: Combine the mechanical equations by substituting the Laplace transform of equation [4] into the Laplace of [3] and solve for current Im(s) . Substituting the above equation and the Laplace of [2] into the Laplace transform of [1] gives . The open-loop transfer function of the DC motor is found by solving for ωm(s)/Vm(s): . Revision: 01 Page: 4 DCMCT Speed Control Laboratory Manual 5. In-Lab Session 5.1. System Hardware Configuration This in-lab session is performed using the NI-ELVIS system equipped with a QNET- DCMCT board and the Quanser Virtual Instrument (VI) controller file QNET_DCMCT_Lab_01_Speed_Control.vi. Please refer to Reference [2] for the setup and wiring information required to carry out the present control laboratory. Reference [2] also provides the specifications and a description of the main components composing your system. Before beginning the lab session, ensure the system is configured as follows:  QNET DC Motor Control Trainer module is connected to the ELVIS.  ELVIS Communication Switch is set to BYPASS.  DC power supply is connected to the QNET DC Motor Control Trainer module.  The 4 LEDs +B, +15V, -15V, +5V on the QNET module should be ON. 5.2. Experimental Procedure The sections below correspond to the tabs in the VI, shown in Figure 2. Please follow the steps described below: Step 1. Read through Section 5.1 and go through the setup guide in Reference [2] Step 2. Run the VI controller QNET_DCMCT_Lab_01_Speed_Control.vi shown in Figure 2. The speed control VI shown in Figure 2 is the top-level VI that will guide you throughout the laboratory. Revision: 01 Page: 5 DCMCT Speed Control Laboratory Manual each step, measure the motor speed, motor current, and stall current. The stall current is measured by holding the load such that the motor is no longer spinning (i.e. stall the motor). Record your results in Table 3. Motor Voltage (V) Motor Speed (rad/s) Motor Current (A) Stall Current (A) -5 -171 -0.189 -1.70 -4 -130 -0.180 -1.27 -3 -89 -0.172 -0.90 -2 -48 -0.169 -0.63 -1 -7 -0.180 -0.26 1 6 0.298 0.27 2 50 0.217 0.76 3 91 0.212 1.05 4 133 0.212 1.43 5 175 0.217 4.79 Table 3 Parameter Estimation Measurements Step 7. Click on Acquire Data after all the measurements are taken to proceed with the laboratory. Step 8. These measurements are used to identify the physical parameters of your par- ticular motor. Later, the mathematical model being developed is used to design a controller. Ensure the same system used to develop the model is also used when implementing the control system. As discussed earlier, there are three model parameters to be identified – electrical resistance, motor torque constant, and the equivalent moment of inertia. Step 9. Recall that the The DC motor's electrical equations are = − − ( )Vm t Rm ( )Im t ( )Eemf t 0 [5] and = ( )Eemf t Km ( )ωm t . [6] As captured in equation [6], if the motor is not allowed to spin (i.e. motor stalled) there is no back-emf voltage. Therefore if Eemf = 0V when I = Istall, equation [5] becomes Revision: 01 Page: 8 DCMCT Speed Control Laboratory Manual = Rm ( )Vm t ( )I stall t . [7] Step 10. The motor resistance can be estimated by copying your stall current measurements from Table 3 into Table 5 and calculating Rm at each voltage step using the expression in [7]. The estimate of the motor resistance can then be found by taking the average over the ten measurements. Motor Voltage (V) Stall Current (A) Estimated Resis- tance (Ω) -5 -1.70 2.90 -4 -1.27 3.15 -3 -0.90 3.33 -2 -0.63 3.17 -1 -0.26 3.85 1 0.27 3.73 2 0.76 2.64 3 1.05 2.86 4 1.43 2.80 5 4.79 2.79 Average Electrical Resistance (Rm): 3.12 Table 4 Electrical Resistance Estimation Step 11. The second model parameter to be found is the motor torque constant, denoted by Kt. Given that in SI units Kt = Km, combining equations [5] and [6] and solving for the torque constant gives = Kt − ( )Vm t Rm ( )Im t ( )ωm t . [8] The torque constant can be calculated at each voltage step using the motor speed and the current recorded in Table 3, along with the estimated electrical resistance in Table 4. The final estimate of the motor torque constant is found Revision: 01 Page: 9 DCMCT Speed Control Laboratory Manual by taking the average of the ten torque constants. Complete Table 5. Motor Voltage (V) Motor Speed (rad/s) Motor Cur- rent (A) Estimated Mo- tor Torque Constant (N⋅m/A) -5 -171 -0.189 0.0258 -4 -130 -0.180 0.0264 -3 -89 -0.172 0.0277 -2 -48 -0.169 0.0307 -1 -7 -0.180 0.0626 1 7 0.298 0.0100 2 50 0.217 0.0265 3 91 0.212 0.0257 4 133 0.212 0.0251 5 175 0.217 0.0247 Average Motor Torque Constant (Kt): 0.0285 Table 5 Motor Torque Constant Estimation Step 12. The final parameter needed to be calculated is the moment of inertia. In the case of the QNET module, there is a disc load fastened to the motor shaft. The moment of inertia of a disc rotating about its center is = Jl m r2 2 . [9] The moment of inertia of the disc used in the QNET systems is 0.000015 kg m2. The motor shaft also adds to the moment of inertia of the system and varies with each QNET module. The total equivalent moment of inertia, Jeq, will be found by fitting the model to the actual system later. Step 13. Click on the Open-Loop Properties tab and the VI shown in Figure 4 should be loaded. Revision: 01 Page: 10 DCMCT Speed Control Laboratory Manual Model Fitted Parameter Measured Value Unit Rm 3.12 Ω Kt 0.0295 N⋅m/A Jeq 1.93E-005 kg⋅m2 Table 6 Model Fitted Parameters Step 21. The Controller Design tab should now be selected. As shown in Figure 6, the Motor Model block is the transfer function representing the open-loop system and the PI Controller block is the control system to be designed. Both blocks are in a negative feedback loop, hence making this system a closed loop control system. By default, the reference input signal is a step of a 100 deg/s. The control system should output a voltage to the motor that ensures the actual motor speed achieves the desired speed. Figure 6 Controller Design Step 22. The two control knobs in Figure 6 change the proportional gain, Kp, and the integral gain, Ki, of the controller. Vary the gains Kp and Ki as listed in Table 7 and record the resulting step response changes and Controller Performance changes. Revision: 01 Page: 13 DCMCT Speed Control Laboratory Manual Kp (V/rad) Ki (V/rad.s) Rise Time (s) Max. Over- shoot (%) Setting Time (s) Steady-State Error (%) 0.00 0.50 0.103 22.300 0.719 0.0 0.03 0.50 0.120 1.050 0.299 0.0 0.05 0.50 0.131 -0.008 0.384 0.0 0.08 0.50 0.135 -0.007 0.581 0.0 0.10 0.50 0.132 -0.006 0.683 0.0 0.05 0.00 0.001 -0.270 0.128 36.3 0.05 0.25 0.334 -0.011 0.990 0.0 0.05 0.50 0.131 -0.008 0.384 0.0 0.05 0.75 0.078 0.724 0.145 0.0 0.05 1.00 0.067 3.980 0.257 0.0 0.55 0.04 0.137 0.274 0.244 0.0 Table 7 Controller Performance Step 23. In general, the type of specification and performance required by a control system varies depending on the need of the overall system and the physical limitations of the system. Find controller gains Kp and Ki that best meet the following requirements for the DCMCT system: (1) Maximum rise time of 0.15 s. (2) Overshoot should be less than 5 %. (3) Settling time less than 0.25 s. (4) Steady-state error of 0 % (i.e. measured motor speed should eventually reach the speed command). Step 24. Once the controller gains yield a closed-loop response that meets the required specifications, enter the Kp and Ki gains used in the last row of Table 7 along with the resulting response time-domain properties. Step 25. Select the Controller Implementation tab to load the VI shown in Figure 7. The controller designed is now to be implemented on the actual QNET DC motor system. The scope in Controller Implementation VI, as shown in Figure 7, plots the simulated motor speed from the mathematical model developed and the actual closed-loop speed of the motor measured by the tachometer. Revision: 01 Page: 14 DCMCT Speed Control Laboratory Manual Figure 7 PI Controller Implementation Step 26. Ensure the proportional and integral gains designed to meet the specifications are set in the Controller Gains panel shown in Figure 7. The function generator in the Desired Speed panel is used to generate the reference speed. Set the commanded speed signal to a square signal with an amplitude of 100 degrees per second. Implement the controller for the same system on which the model was obtained. This ensures the controller is not based on a model that may not represent your motor. Step 27. If the simulated or actual closed-loop response no longer meet the requirements, tune the controller in the Controller Gains panel. Record the final Kp and Ki used and the resulting control performance properties of the closed- loop response – rise time, overshoot, settling time, and steady-state error in Table 8. Revision: 01 Page: 15