Lab 2 Handout - Winter 2024 (1)

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Oregon State University, Corvallis *

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437

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Mechanical Engineering

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Apr 3, 2024

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pdf

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- 1 - MFGE437 Lab 2 – Machine Tool Feed Drive Axis Identification & Control (Actual Lab takes place on 2/12 at ATAMI on HP Campus) Lab TA: Kaan Bahtiyar bahtiyak@oregonstate.edu This laboratory project has a PRELAB. The highlighted text below indicates the PRELAB (30% weight) that you need to complete. The prelab must be done coming to the lab. The aim of this lab project is to identify dynamics of a ball-screw driven machine tool axis dynamics and design motion controllers to achieve a desired dynamic characteristic. The system used in the lab is depicted in Figure 1. Figure 1: Experimental laboratory servo motor setup used Figure 1 shows the detailed schematic of the experimental setup featuring a single-axis ball-screw drive. As shown, machine table can move in only one direction, driven by a ball-screw mechanism similar to what has been demonstrated in the class. Rotary encoder is attached to measure the position of the motor shaft. The electrical motor is driven by a servo amplifier. This means, once voltage is sent to the amplifier, the amplifier generates current to the motor windings. Once the motor receives the current, it generates torque based on the motor torque constant and rotates the ball-screw. The feedback control of the motor is achieved by a PC. The PC is equipped with a data acquisition system. 1. Identification of Motor Velocity Dynamics In order to design a motion controller and achieve desired performance, dynamics of the motor system/axis of the machine needs to be identified. As studied in the class, velocity dynamics of the motor system is considered as a 1 st order system. Simplified block diagram of the system is presented in Figure 2. Figure 2: Velocity dynamics of the motor G v ( s ) = K v τ v s + 1 First Order System u[v] (Voltage to Amplifier) !̇ [mm/sec] (Moto/Axis Speed)

- 2 - An experimental method to identify dynamics of the system is to simply send a step (constant) voltage and measure the time constant and velocity gain K V from velocity response. As shown in Figure 3, when a voltage is sent to the amplifier, the motor of the ball-screw axis starts to speed up with an exponential function showing the first order system dynamics characteristics. a) Theoretical Response b) Measured Speed Response on the Lab Setup Figure 3: Characteristics of the 1 st order velocity dynamics of the motor/axis system Pre-lab Tasks (These has to be done and presented to the TA during the lab as a group) 1. Data associated with Fig. 3.b (axis velocity) is uploaded on Canvas in an excel file. Please use this data (excel file) and identify the time constant and the velocity gain K V of the lab setup by “eye-balling”. Lab groups are given at the last page of the handouts. 2. Use identified parameters and simulate speed response of the model to a 0.15[V] step voltage command. Once you simulate the response, compare measured (see Fig. 3.b) and simulated responses by plotting them on top of each other. The objective is to see how well they match each other. If they do not match at all this means you were not able to identify the parameters correctly. Please note that, you need to have those values with you during the lab. Present your results, including the figure displaying both the experimental and simulation of identified system responses overlaid on top of each other, to the TA. Therefore, you must complete this identification procedure before the actual lab. τ v τ v

- 3 - 2. Velocity controller design: The velocity dynamics of the axis system is identified in the previous section based on experimental data . This part of the laboratory assignment is for you to implement a proportional velocity controller based on the identified velocity dynamics. The block diagram of the feedback control system is given in Figure 4. Figure 4: Closed loop Proportional Velocity control Pre-lab Tasks (This has to be done and presented to the TA During the lab as well) As shown, the Kp proportional gain multiplies the position error ( e ) and generates voltage to drive actual motor velocity close to the reference. Derive the transfer function of the closed loop system and calculate feedback control gain Kp to achieve the desired time constant of t des = 0.2[sec] before you come the lab. During the lab, TA will implement your controller. After you implement the proportional controller during the lab, you need to comment on the results in your lab report . How does the resultant system behave? Perform a simulation and compare them together with the measured speed and comment on the differences. What can cause those differences? Using final value theorem calculate the final motor velocity in rpm. Compare it to the measured motor velocity when you implemented your controller. 3. Effect of Load Change on Motor Dynamics Once you designed your feedback gain for the single axis setup, you will then be asked to implement the controller by removing mass from the setup. You will run your velocity controller again without changing the Kp gain. As a result, the response would be different, and you will measure the step response again. Determine the new time constant of the new closed loop system . Your task is to mathematically show whether the new time constant should be less than the desired time constant ( t des ), or more. Clearly show your calculations. How much did the time constant and the final value of the system for a step response has changed? Comment on the response of the system. Hint: Compare closed loop transfer functions for both setups for the same K P . 4. Position Controller Design In this experiment, you will inspect response of a position controller to the servo system. The block diagram of the system is given in Figure. Figure 5: Closed loop Proportional Position control of servo motor During the lab, the TA will tune a position controller. He will record the response of the system to a step position command. TA will provide you the measured response of the system in .csv file. K v τ v s + 1 Kp u e − Motor/ Axis Velocity Reference Velocity K v τ v s + 1 Kp 1 s u e − Motor/ Axis Position Reference Position !̇ ! x r

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- 4 - In your lab reports, please calculate the rise time and overshoot of the system for this Kp gain. Compare the calculated response to the measured response. How big is the error? What would cause the difference between calculated response and the measured? Please provide engineering comments. Lab Procedure and Report Preparation This lab requires a prelab to be performed. Please prepare your prelab and consult with the TA. During the lab, please follow TA’s instructions. Your lab report should be presented as an engineering report. It should have 3 sections. Namely, Introduction, Main Body and Conclusion . In the introduction, please summarize the objectives of this lab. In the main body section, explain about the lab tasks, how you performed them. Show your calculations clearly. Be concise. Point out any difference between calculations and the actual measured quantities. Why are they different? Elaborate on them. In the conclusions section, present your final thoughts. Labs will take place on HP Campus B11, also known as the ATAMI building. Details will be given in the announcement. Lab Groups Section 010 2pm-3:50pm in ROG 126 - Rogers Hall 126 Section 011 4pm-5:50pm in ROG 126 - Rogers Hall 126