Mechatronics Demonstrator 2002ME 505

1. Description

In this project you will assemble and calibrate a mass-spring-damper mechatronics demonstrator system and perform a model based control system design and implementation using visual programming.

You will receive the mechatronics demonstrator system in “kit” form. Each kit consists of four major components, (1) the mechanical mass-spring-damper assembly, (2) a displacement sensor, (3) a voice coil actuator, and (4) a voice coil power amplifier. A photograph of the assembled system is shown in Figure 1

Figure 1: Mechatronics Technology Demonstrator System

The primary mass element in the system is the voice coil. The spring effect is provided by the 4 supporting wires and the damping effect by the “flexing” of the 4 “L” brackets securing the device to the plywood base.

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The operation of the system is based on forces produced by the magnetic voice coil actuator which, in turn, produce vertical motion of the suspended mass. Vertical displacement of the mass element is then sensed using a PSD (Position Sensing Detector) sensor. Both the sensor and actuator are interfaced to a PC based visual programming application “VisSim” using a National Instruments PCI-6024E Data-Acquisition Board. All control and monitoring tasks will be accessible through the VisSim application.

Class teams will used UT 106 and Dana 102 facilities to assemble, calibrate, and perform experiments on their mechatronics demonstrator. A total of 14 computers are available in these labs. After a team is has completed their experimental work, their mechatronics demonstrator must be disassembled and stored in UT 106.

2. Assembly Information

Step 1: Mass-spring-damper system assembly: (Kondo’s instructions). Verify the mass oscillates freely when displaced by hand. You should observe at least 100 perceptible oscillations for normal displacement inputs. If the number of oscillations is significantly less, check for the alignment of the voice coil actuator and the magnet.

Step 2: PSD sensor unit: Attach the PSD sensor unit to the mass-spring-damper system. Be careful, if improper or rough handling damages the PSD, the group will be charged for a replacement. Install the laser pointer in the PSD sensor unit. Check the alignment of the laser with the PSD. The PSD output signals are wired to the National Instruments CB-68LP screw terminal board. Create a VisSim diagram with two real time inputs to measure the output voltage of the PSD. Verify operation of the channels and calibrate the input into engineering units.

Step 3: Voice Coil Actuator: This consists of three substeps; (1) mounting and alignment of the voice coil, (2) mounting of the power transistor, and (3) assembly and mounting of the drive circuitry.

Figure 2: Voice Coil Mounting and Alignment

NPN and PNP power transistors are mounted on the top of the metal enclosures as shown in Figure 3.

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Figure 3: Mounting of the Power Transistors

A power transistor driver circuit is built using the breadboard according to the following circuit shown in Figure 4.

Figure 4: Driver Circuit Schematic

A photograph of the “breadboarded” driver circiut is shown in Figure 5.

Figure 5: Breadboard of Driver Circuit

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Once you have completed the assembly and testing of the mechatronics demonstrator system, verify the assembly and results with the lab instructor before continuing with any experimental work.

3. Model Based Control: Experimentation & Analysis

This step consists of two tasks; (1) development and validation of a dynamic model of the mass-spring-damper system, and (2) development, implementation, and validation of a control scheme which modifies its behavior.

3.1 Dynamic ModelingThere are two modeling options, physics based modeling and empirical modeling (using Auto Regressive Moving Average (ARMA) modeling and least square identification). You are required to select one of the options, develop the model, and validate its performance from data obtained from the actual the mass-spring-damper system.

Option A: Physics Based ModelThe physics based model for the mass-spring-damper system will be based on the mechanical illustration shown in Figure 2.

Figure 2: Mass-Spring-Damper Mechanical Illustration for Physics Based Model The resulting physics based model will produce a transfer function relating input force to the mass to output displacement.

The mass, M, and spring constant, K, are values which can be measured. A precision scale is available in the lab for calculation of the voice coil mass (M). The same device will also be used to estimate the spring constant by applying a measured weight and measuring the spring delta displacement. The damping, B, cannot be measured directly and will be estimated from the experimental data to match the decay time of the exponential envelope.

Validation of the physics based model will require comparison of model and true system responses (vertical displacements) obtained from identical forcing functions (forces applied to the voice coil).

Option B: Auto Regressive Moving Average (ARMA) Model with Least Square IdentificationParameters in a second order ARMA model will be identified from experimental data using least squares identification. Although the data can be recorded using the VisSim application, teams are strongly encouraged to used MatLab (or a similar matrix program) to perform the least squares fit.

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Figure 3 presents a diagram of how experimental data for the ARMA modeling could be collected using the VisSim application. The input signal, called r(t), generated in the block named “Input”, could be defined as a series of randomly spaced and amplitude steps filtered through a low pass filter.

Figure 3: Data Acquisition used in the ARMA model

For successful ARMA modeling it is essential that the input signal contain sufficient frequency content to excite the dynamics of the plant, ie; r(t) should not be set as a unit step. The data from the block diagram is exported to an ASCII file named “c:\temp\ry.dat”. This file is then loaded into MATLAB for solution of the model parameters. The form of the ARMA model will be;

Once the ARMA model parameters have been calculated, the model will be mapped from discrete to continuous time using trapezoidal (bilinear) approximation. For this approximation, the unit advance operator, E, is defined in terms of the differential operator, D, as;

Substituting this into the ARMA Model transfer function will produce a second order continuous transfer function that will be validated with data obtained from the experiment.

3.2 Control

There are three control options, any of which could be used to modify (attenuate) the natural motion behavior of the mass-spring-damper system; (1) tri-state control, (2) rate feedback control, and (3) cascade lead control with both continuous and discrete implementations. For the control option selected you will (1) design the control logic, (2) implement the logic in the VisSim application, and (3) obtain comparison results between the controlled and uncontrolled system to present the improvement in performance. In part 3 you must design, as part of the control, an algorithm capable of “injecting” a controlled and repeatable disturbance into the system for comparison.

Option A: Tri state control This on-off control design has two “on” states; full on in the + direction and full on in the – direction. The resulting control is called tri-state, the third state being the “off” state. The algorithm you design will sense peak points of mass acceleration in either direction, negate them, and feed this information back to the actuator which will, in turn, attenuate the acceleration bringing the mass to rest in a short amount of time.

Option B: Rate Feedback Control Rate feedback is the simplest type of feedback control which will attenuate vertical. It is essentially a continuous version of the tri-state control and uses a derivative operation to estimate the vertical velocity of

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the mass. Operation of the algorithm will require estimation of the derivative of the “x” displacement signal and feedback of the negative of this rate signal back to the actuator through a rate feedback gain. This gain as well as the derivative estimation will be the major design elements of this task.

Option C: Cascade Lead Control with Continuous and Discrete Implementation Cascade lead control serves the same function as the rate feedback control without the need to explicitly differentiate the vertical displacement signal. Instead, a forward loop first order compensator (cascade lead compensator) identical to a high pass filter, is designed having one pole and one zero. The break frequency of the zero will be 1 rad/sec and the break frequency of the pole will be 100 rad/sec. Once you have completed the design, implementation, and validation of the continuous lead controller it will be converted to discrete time using bilinear mapping, re-implemented and re-validated.

4. Reporting

Each team will be required to submit a written report describing their experiment and conduct a 30 minute presentation of their experiment and findings. Reports and presentations will be submitted both typed and electronically. The following format will be used for the reports.

Executive Summary: 1-2 paragraphs describing the experiment and results.

Objective(s): (1 page) State the goals of the experiment, these should include the objectives of the modeling and control options as well.

Assembly Information: (3-4 pages) Concise step-by-step summary of the assembly, problems, workarounds. This section should be divided into three subsections; (1) mechanical system assembly and validation, (2) sensing unit assembly and validation, and (3) actuation system assemble and validation.

Analysis: (4-6 pages) Depending on the modeling and control options selected, this section will include all analysis and implementation steps.

Results: (3-6 pages) As they pertain to your objectives, must include plots, diagrams, and text. References to similar experiments are encouraged – check library/internet for these.

Recommendations: (1 page) Summarize all workarounds to problems and objective commentary on alternate solutions/improvements to the experiment.

5. Additional Information

The kit will include all components necessary to assemble the mechatronics demonstrator. If the PSD or any other component is damaged through handling, the team will be required to purchase a replacement. A price list for the individual parts is included below.

1. Electrical ComponentsSub-Total

Position Sensing Detector (PSD) UDT PIN SL5-2 $24.50 $24.50Laser Pointer RadioShack Number 63-1046 $29.99 $29.99Power Transistor 2N3005 , NPN RadioShack Number 276-2041 $1.99 $1.99Power Transistor MJ2955, PNP RadioShack Number 276-2043 $0.97 $0.978 inch Subwoofer PRO-CSW800 RadioShack Number 40-1017 $59.99 $59.993, Metal Enclosure RadioShack Number 270-235 $1.99 $5.97Modular IC Breadboard Socket RadioShack Number 276-175 $7.99 $7.99Toggle Switch RadioShack Number 275-603 $1.69 $1.69

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2, Coaxial DC Power Jack RadioShack Number 274-1576A $1.69 $3.389V Snap Connector RadioShack Number 270-325 $1.39 $1.39Battery Holder RadioShack Number 270-382 $1.29 $1.29CB & Ham Microphone Plug RadioShack Number 274-001 $1.99 $1.994-Pin Panel Mount Jack RadioShack Number 274-1576A $1.99 $1.992, AA Battery (2 Per Pack) RadioShack Number 23-872 $1.79 $1.792, 6V 300mA Power Supply RadioShack Number 273-1758 $8.99 $17.98

2. Mechanical Components

4, GHS 0.026 inches diameter Guitar String $0.64 $2.56

4, 8 inch Brace $4.97 $19.888, 5 inch Brace $1.95 $15.604, Anchor $0.32 $1.28

3, 2 inch Brass Brace $0.28 $0.84

Brass Laser Bracket $1 $1Aluminum Sensor Unit Tray $2 $2Aluminum Speaker Suspension Bracket $1 $1

3. Miscellaneous

Wooden Baseboard $5 $5Total Cost $212.06

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