Motor-Propeller Damped Compound Pendulum

Figure 1: Low cost and maintenance, easy to assemble and store system ideal for
reinforcing classroom theory in dynamics and control design.

Motivation and Audience

• an easy-to-setup, low-cost and low-maintenance experiment platform
• small footprint
• hands-on system identification and PID control experiments
• open-source hardware and software
• off-the-shelf components and minimal machining with widely available shop tools
• expandable with examples in adaptive, fuzzy and sliding-mode control

The photo above (Figure 1) showcases a platform used at Drexel University's Mechanical Engineering Department. It's 5 parts quickly assemble into a damped compound pendulum with a motorized propeller at one end. The photos below (Figure 2) illustrate the speed and ease of moving from storage to setup in 10-minutes.

Figure 2: The system is compact and can be easily and rapidly assembled or stored away

A spring desk clamp secures the pendulum to a table. Turning the power supply on starts the motor. The propeller generates lift and induces a torque about the pivot. This torque makes the pendulum rotate counter-clockwise (right). In lab, one designs controllers to achieve desired transient and steady-state responses. This platform's simple construction is robust, assembles and stores away easily, and has been used successfully to demonstrate PID (MEM 351 Undergraduate Dynamic Systems Lab) and fuzzy, sliding mode and adaptive controllers (MEM 800 Graduate Advanced Control Techniques).

This article breakdowns as follows:

• Underlying Theory and Objective
• Parts List and Sources
• Construction
• Controller Design
• Final Words
• Appendix

Underlying Theory

Figure 3 is a photo sequence. From left to right: the motor is first turned on, the pendulum rotates counter-clockwise, falls clockwise, then rotates counter-clockwise again. The oscillations decay exponentially to a steady-state angle as seen in this video. The step response graph shown in Figure 4 plots the pendulum angle after 2 Volts is applied to the motorized propeller. The angle was captured using an optical encoder mounted on pendulum pivot.

Figure 3: Applying a step voltage results in pendulum oscillations. Click video to see.

Figure 4: Step response plot of pendulum angle in degrees versus time in seconds
Angle settles to 50 degrees in 30 seconds. Motor voltage killed after 30 seconds.

The dynamic equations of motion, block diagram and constants are described the following two PowerPoint slides (Figure 5 below). Essentially, a small angle approximation is used to linearized the dynamic equations of motion. Also assumed is the torque is proportional to motor voltage.

Figure 5 PowerPoint Slides showing open-loop block diagram

Objective

Parts List and Sources

Figure 6: With a PC, data acquisition hardware and apx. $200
in parts, an effective lab experiment can be assembled.

Every effort was made to find a single source supplier for all parts. One will note that many of the parts, like resistors, capacitors and screws are common items in engineering supply rooms. PVC bar stock and L-brackets are often found in engineering machine shops. US-based vendors include Jameco, National Instruments, McMaster-Carr, US Digital, Small Parts, C&S Sales, Radio Shack and Hobby Lobby

Motor and Propeller Choices

Table 2 lists parts to construct a 3 Amp power op-amp. The section on construction provides the schematic and PCB artwork. The listed power supply has both fixed and adjustable outputs and hence pricey. Any DC power supply that provides 5 Volts at 3 Amps should work fine.

Data Acquisition and Power Supply Choices

Construction

Pendulum

Figure 7: Pendulum Bar
Click here for SolidWorks eDrawing Animation

Figure 7 illustrates the main part of pendulum; a 19.5 inch long piece of PVC. The 0.25-inch diameter holes provide a wide range of points to mount the pendulum onto the encoder shaft. The motor straps onto the area that has been milled out (see below). Dimensioned machine drawings for the above part and the encoder base are given below:

Motor Prop

Figure 8: Motor Prop Setup

The prop adaptor press fits onto the motor shaft as shown in Figure 8. The propeller is held between collet, washer and nut. For this particular propeller, the front side is the one with text on it; as the propeller rotates clockwise (looking from motor shaft side), the pendulum will try to rise. The velcro is screwed onto the pendulum and wraps around the motor to keep it secure.

Encoder Base

Figure 9: Encoder Base

Electronics

Figure 10: Power op-amp schematic. Click here for PDF Version

Figure 11: PCB populated with components

One could wirewrap or breadboard this schematic. Alternatively a printed circuit board (PCB) can be homebrewed or professionally fabricated. Figure 11: depicts two views of a PCB that was fabricated at AP Circuits. The PCB artwork is depicted Figures 12 and 13 (shown at 2X scale) and can be etched at home. For convenience the zip file mem351-022305.zip can be emailed of FTP'ed to AP Circuits and fabricated for about $10 USD per board.

Figure 12: Solder Side shown at 2X scale. Click here for PDF

Figure 13: Component Side shown at 2X scale. Click here for PDF

The PCB also includes pads to include parts for an encoder filter (as given in Table 2). The LS7804 (data sheet) is an encoder-to-counter chip that performs debounce and filters for jitter. Without this chip, miscounts are very likely. The LS7804 also can increase one's encoder resolution four times. As such, a 3-pin header and jumper was used (see Figure 11 above) so that one can use the encoder or is (X1) or at 4-times resolution (X4). The schematic in Figure 14 provides details and pin connections to a PCI-6025E NI-DAQ card.

Figure 14: Encoder Filter. Click here for PDF Version

Final Assembly

Figure 15: A spring clamp (left) holds the encoder base onto the table (middle)
and the pendulum is then screwed unto the encoder shaft coupling (right)

The three major components (pendulum, motor-prop and encoder base) assemble together as illustrated in the photo sequence (Figure 15 above). Two more compoents (power supply and driver PCB) require the following connections. The motor leads connect to the +MTR and -MTR headers on the driver PCB. The encoder is attached to the PCB via a 5-wire ribbon cable. Lastly, the power supply connects to the PCB on the headers labeled PWR and GND. The net effect is 5 components that can quickly assemble for a lab or dis-assemble for storage.

Controller Design

Figure 16: PID response with low overshoot and fast transient response. Click for video.

PID Control

Figure 17: PID block diagram. Click for Simulink file pidpendulum1_0.mdl.

One notes that right after the PID calculation, there is a gain of 2/55 Volts/deg. This gain is a simple model for the motor; this assumption is that motor reaches speed instantaneously. A first-order model that includes the motor's time constant would be more accurate and would be an excellent lab exercise.

One advantage of PID control is that a complete system model is not needed before actual implementation. With that in mind, a LabVIEW program can be quickly created. Figure 18 depicts the graphical front end. One notes PID tuning knobs and text boxes to define the setpoint angle and monitor the pendulum's actual angle. Figure 19 is the LabVIEW block diagram. Here, DAQ Assist was used to aquire the encoder angle and write the values to a measurement file.

A case structure is applied to the encoder angle input. This is transform the angle into a desired coordinate frame; pendulum at rest is called 0-degrees, and the angle increases when rotation counter-clockwise (i.e. positive theta) as drawn in Figure 5. Also within the case structure, the raw angle is divided by four because the jumper on the encoder-to-counter filter (Figure 11) is set to X4 resolution.

A general rule of thumb in control design is to sample at least 4 to 20 times the rise time. The open-loop step response (like Figure 4) yields a 2.5 second rise time. As such, the sampling time should be at least 0.125 to 0.625 seconds. In LabVIEW, the Wait Until Next ms Multiple was set to cycle the while loop every 25 milliseconds, which is more than fast enough for closed-loop control.

Figure 19 also shows the PID gains, which use a shift register to differentiate and integrate the error. Figure 16 shows excellent results. This video shows the effects of changing the PID knobs in the front end. This pendulum is a Type 0 system) and hence sensitive to integral gain. The video shows the pendulum going unstable as integral gain is increased. Derivative gain will help kill oscillations and steady-state error but at the cost of longer settling times.

Figure 18: LabVIEW Front Panel. Click for VI file pidPendulumRecord1_0.vi

Figure 19: LabVIEW Front Panel. Click for PDF

Final Words

Many interesting experiments, for reinforcing classroom concepts, can be developed. The platform can also be easily modified to investigate complex and higher order systems. At Drexel University, topics like sliding mode, adaptive, fuzzy and lead-lag control were conducted with this platform and listed in the Appendix

National Instrument's USB-6008 data acquisition unit can yield new paradigms in teaching control system design. Costing less than some engineering textbooks, each student can buy a USB-6008 for class. Alternatively, units can be lent to students each term through the department's lab supply room. Students can then use their laptops to perform system identification, design controllers and validate performance. Critical to such hands-on experiential learning are rugged yet simple and easy-to-use platforms, like the one featured in this article.

Appendix

• video of open-loop pendulum system
• video of controlled pendulum
• SolidWorks eDrawing animation of pendulum bar
• mem351-022305.zip PCB files. Can be sent to any PCB fab house e.g. AP Circuits
• PCB solder side artwork (2X scale)
• PCB component side artwork (2X scale)
• LS7804 data sheet
• Simulink file for PID control
• LabVIEW VI file for PID control
• Drexel University MEM 351 lab notes on PID Experiment
• Pendulum Experiments (includes videos and code) with
  • Fuzzy Control
  • Model Reference Adaptive Control (MRAC)
  • Lead-Lag Control
  • Sliding Mode Control

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