Transcript
Lab 18 Grading Rubric Student Name:
___________________________________________________________________
Grading Item Derivation of closed loop transfer function Comment on the conditions required for the closed loop to be stable
Point
Total 5 5
Analysis: Steady-state performance for a step input
Final value theorem
5
Comment on the effect of Kp
3
Implementation: Plot of step or square wave
4
State pole locations for Kp and Ki values
3
Comment on the effect of the gain on the transient response
3
Analysis: Steady-state performance for a ramp input
Final value theorem
Implementation: Plot of ramp response
5 3
Analysis: Steady-state performance for a constant disturbance
Final value theorem
5
Implementation: Plot showing PI controller rejecting constant disturbances
3
Implementation: Plot comparing step or square wave with Kp and Ki turned for damping-ratios State damping ratios and corresponding Kp and Ki values
4
Observed response consistent with expected result? – comment on discrepancies Implementation: Plot of tracking performance
3 4
Triangular
3
Sinusoidal
3
Analysis: Derivation to predict performance when the controller output scaled by 2 Implementation: Plot showing experimental and simulation data
5
Total
70
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ME 5241: Computer-aided Engineering Homework 1: Motor Torque Analysis
Spring 2015 January 26, 2015
Background1 A 2-Axis SCARA Robot (Fig. 1, right) Has a ground pivot motor, and a second motor at the articulation point between the grounded link (link1) and the floating link (link2). The robot is used for “pick and place” type operations, and for this application will carry a 5 kg payload at the end of link 2. For diagnostic and modeling purposes, the robot is exercised at constant angular Figure 1: SCARA Robot
velocity.
An estimate is required of the motor torque as a function of the “shoulder” angle theta1 (i.e. the angular position of link1.) Assume the masses of the links are negligible compared to the payload, and focus on the ground pivot motor (the “shoulder” motor) at the base of link1. Also estimate the inertial force exerted by the payload.
Figure 2: Schematic of the 2-axis Robot 1 The robot shown here is an Epson G-Series 2-axis SCARA Robot; see http://robots.epson.com/productdetail/5
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Objective: Write a Matlab program that estimates the inertial force and also the torque required at θ1 to move the SCARA robot of Figure 2 at constant angular velocity. The motor torque curve and the inertial force curve are plotted simultaneously on the same plot. As shown in Figure 3, both vertical axes are used to plot the two quantities 2, and a legend is provided. A plot for one full revolution of the “shoulder” motor is required. Parameters, naming conventions and default values are all given in the accompanying document, “HW1_PartialSolution.pdf.” The graph should be titled, the grid turned on, the axes labeled and a legend provided. See the “rubric” section further down in this document. A sample plot is shown in Figure 3 below.
Figure 3: Sample Output Programming A portion of the program will be provided: you are free to use this, or start from scratch. Please refer to the "HW1PartialSolution.pdf" document for a discussion and code listing. Manual Check Verify your program is working properly by working through a particular configuration (theta1 = 30 degrees) and verifying your program's result matches your calculated 2 Use matlab help function “>> help plotyy” and “>> help legend” for assistance.
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result. Verification is an important task when writing a program that will eventually be used to make design decisions! Include your calculation in an appendix in your memo. Note: the hand calculations may be written out and scanned – they do not need to be entered into a word processor. Deliverables: Due Monday, February 2, 2015 (uploaded before the start of class) Please upload an appropriately named zip file containing the following two items: 1. Memo and any appendices 2. Copy of program and function m-files The zip file should have your initials, an underscore, and the label “SCARA1”. My uploaded zip folder, for example, would be named: “FMK_SCARA1” Each of the two deliverables are described in more detail below. 1. Brief (one or two page) memo reporting your results Write a brief (one or two page) memo documenting your results. Include a plot of torque vs theta in the memo. Use the short memo format documented in the “memo guidelines” document found on our course website (“MemoGuidelines.pdf”). Your memo will include a plot of your results similar to Figure 3 above. The memo will also include at least two appendices: the program listing, and the hand calculation corroborating your result. The hand calculation does not have to be entered into a word processor. 2. “scara.m” Program m-file Make sure your program is well-commented, and you’ve chosen meaningful names for your variables. Name your program “scara.m” : the grader will be running your program.
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Homework 1 Rubric This homework is worth 10 points, distributed as follows: [2 pts] Deliverables: received on time [1 pt] memo with manual verification appendix (uploaded at our course website) [1 pt] “scara.m” Program (uploaded at our course website) [4 pts] Programming [1 pt] Matlab script m-file named “scara.m” [1 pt] produces a correct plot of torque (Nm) versus “shoulder” angle (in degrees) [1 pt] produces a correct plot of force (N) versus “shoulder” angle (in degrees) (on the same plot) [1 pt] program is well-commented, uses meaningful variable names [4 pts] Results [1 pt] Short memo (in the specified “short memo” format3) describes context and results for homework 1 [1 pt] Graph is titled, axes are labeled, grid is turned on [1 pt] Legend is provided, and both vertical axes are employed to display results [1 pt] manual verification complete, provided in the appendix
3 See “MemoGuidelines.pdf” found in the “documents” folder on our course website.
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University of Michigan - Center for Research on Teaching and Learning (CRLT)
