Experimental Data Motor Control System

Control System Overview

The displacer in the prototype engine is driven by means of an electronic stepper motor. Stepper motors allow precise position control as they move one ‘step’ at a time. In the case of the motor used here, a step is 1.8°, and within that step a ‘microstep’ resolution can be defined, down to as little as 0.014°. This is essential for the displacer control as the displacer needs to be moved between a 120° swing in a reciprocating manner.

Experimental Data Motor Control System

Figure 71: Control system block diagram

Operation of the motor control and drive system is illustrated in Figure 71. The motor is energised through the driver, which sends the appropriate power to the windings depending on the step and direction inputs from the controller. The controller takes several inputs and sends the appropriate signals to the driver based on the code which it is programmed with.

Control System Operation

The control system operates in open loop control. This means that feedback is not taken into account by the controller, but the motor just moves through x number of steps that correspond to 120°, then back again. The advantage of this type of operation is its

Simplicity, the downside being a lack of reliability. Under open loop control if the motor misses steps, stalls or overshoots its position target, then the controller doesn’t ‘know’ that something has gone wrong, and just keeps on trying to move the motor back and forth by 120°. Obviously it would be preferable to use closed loop (feedback) control however the controller used does not facilitate support for this. Fortunately, the scenarios in which open loop control fail are reasonably rare, meaning a rather elegant solution presents itself in the form of using the limit switch inputs of the controller as a form of pseudo-feedback. If the motor drives the displacer too far then it will trip one of the limit switches (pictured in Figure 72), causing the motor to stop abruptly and reset the position counter. This means that even if position drift from dropped steps occurs over time and it eventually reaches the point where it is a major problem (activating a limit switch), then it will be reset back to zero again.

In order for the controller to know when to start moving it is necessary to have some sort of trip signal based on the position of the crankshaft. This is achieved by using an opto-sensor (pictured in Figure 72) which consists of both a light source and light detector, such that when a reflective surface is near enough it will send a high signal. The crankshaft has a small ring fitted to it near to where the opto-sensor is mounted. This ring is dark in colour and has two small reflective strips 180° apart from each other which signal the start of displacer motion in the clockwise and anti-clockwise directions respectively. The ring has a grub screw allowing it to be rotated, thereby effectively allowing adjustment of the phase angle between the piston and displacer.

Experimental Data Motor Control System

Figure 72: OPB770TZ Optical sensor (left) and SPDT microswitch (right)

The flow chart in Figure 73 shows the control algorithm used by the controller. The startup routine consists of rotating slowly in the anti-clockwise direction until a limit switch is reached, then backing off that limit by a small margin so that the displacer is at the position known to be its correct anti-clockwise end point. From here it moves based on a trigger signal from the opto-sensor, based on crankshaft position. A direction flag is set after each move to ensure that the displacer moves in the correct direction on its next trip.

Experimental Data Motor Control System Experimental Data Motor Control SystemYes

F ‘N

Back off limit

J

By margin

Set direction flag to clockwise value

подпись: set direction flag to clockwise value
 
Rotate through 120° anti­clockwise ▲

Rotate through 120° clockwise, set direction flag to anti-clockwise

Experimental Data Motor Control System

Yes

It is necessary to fully test the control system before implementing it into the engine. The motor/gearbox combo was tested in the test rig setup to see what sort of speeds and acceleration could be obtained. The flywheel from the engine was attached to the gearbox shaft to approximate the inertial load of the displacer. The inertia of the flywheel slows the acceleration of the motor, which during testing is trying to oscillate through 120° at the output shaft at the maximum possible speed. The gearbox is a low-backlash inline planetary gearbox with a 10:1 reduction ratio. This increases the available torque from the motor but sacrifices its speed, both by a factor of 10.

Experimental Data Motor Control System

Figure 74: Motor and gearbox set up on the test rig, flywheel mounted as dummy load

The moment of inertia I of the flywheel is approximated as:

/ =-m(r;2 + r02) (57)

Where m is the mass of the flywheel and ri is the outer radius and ro is the inner radius of the solid ring. This calculation ignores the small contribution of the spokes in the flywheel. With a mass of 12 kg, outer radius of 150 mm and inner radius of 125 the moment of inertia is calculated as being 0.23 kg. m2.

The moment of inertia of the displacer can be calculated as for a solid cylinder with a radius of 400 mm:

(58)

подпись: (58)/ = — mr2

A sample block of expanded foam was weighed and measured, showing a density of 35 kg/m2. The volume of the displacer is 0.13 m3, giving it a total weight of 4.5 kg. This makes the inertia for the displacer 0.36 kg. m2, a value about 1.5 times that of the flywheel used for testing. Even though the flywheel does not equal the displacer’s inertia (and ignoring the
effects of mechanical friction of the seals), the flywheel still provides useful information about the capabilities of the motor and gearbox.

It was found in testing that the maximum speed of the motor was the parameter holding back its performance the most, rather than just its acceleration. The speed setting of the controller was set at 34,000/4 SPS, or 8500 steps per second. This was the maximum speed that could be obtained without motor stalling occurring. This setting was used with the driver at half step resolution, giving 400 microsteps per revolution (0.9° per microstep). This means that 8500 SPS equates to about 6.3 rad/s angular velocity. Through the 10:1 reduction gearbox this gives 0.63 rad/s on the output shaft, hence it will take 0.16 seconds to rotate through 120° (1333 microsteps) at full speed (ignoring ramping).

Ramping

For a displacer speed of 2 Hz the process of ramping up to full speed, travel at full speed and ramping down to a stop again must occur in the space of 0.25 s, and preferably less as the faster this process takes place the better the approximation to the ideal discontinuous motion.

By using the information available for motor torque and load inertia, the maximum acceleration possible can be calculated:

(59)

подпись: (59)T

A = l

Where t is the motor peak torque available at the shaft (motor torque x gear ratio) and a is the angular acceleration of the motor shaft. The result of this calculation is a maximum acceleration of 526 rad/s2.

The maximum ramping obtained without stalling was with the settings at K=6/2, where 6 is the acceleration parameter and 2 is the deceleration parameter. It is easier to decelerate the load than accelerate it, hence why the deceleration has a steeper slope than the acceleration. An acceleration parameter of K=5/2 was tested with the flywheel load and while it worked most of the time it would cause stalling occasionally, hence the lesser value (6) was taken as the maximum possible acceleration.

An acceleration parameter of 6 equates to approximately 30,000 steps/s2 as measured (this value had to be measured as the value of K has no rational units — it is defined as being the delay time between increments in speed, where the increment is undefined). This translates to an acceleration of 471 rad/s2 at the output shaft. An acceleration — K parameter of 5 equates to 565 rad/s2.

The maximum deceleration parameter is theoretically zero, i. e. an instantaneous or ‘hard’ stop. While this is somewhat achievable it will adversely affect the life of the displacer and the motor and gearbox components through the large forces experienced in such an abrupt stop. In regular use, even with a non-zero value of deceleration, it is still likely that hard stops will occur at such times as when a limit switch is hit or if the optical sensor is triggered before the end of travel is reached (see Section 4.1.2).

Using the values already calculated for load inertia and motor torque, the graph in Figure 75 was produced. The blue line shows the motion achievable under maximum acceleration and speed conditions — it is clear that the torque and/or speed of this setup is insufficient to drive the displacer at the desired operating speed. At this operating speed the displacer is unable to complete its full range of motion. The red line shows the predicted motion if two motors with a lower gearing ratio of 2:1 were used instead. Clearly this is a much more preferable motion profile, as it gives the desired discontinuous motion by being able to move the load faster. This graph is produced using the inertia figure for the dummy load (the flywheel).

The second graph, Figure 76, shows the same load and motive sources operating at the reduced speed of 1.5 Hz. This is the maximum speed achievable by the single motor while still moving through the entire 120° motion.

Figure 75: Displacer profiles at nominal operating speed with dummy load

подпись: figure 75: displacer profiles at nominal operating speed with dummy load

Dispalcer Motion Profiles Operating at 2 Hz

Experimental Data Motor Control System

Time (s)

Single Motor, 10:1 Gearing Dual Motors, 2:1 Gearing

Dispalcer Motion Profiles Operating at 1.5 Hz

Experimental Data Motor Control System

Time (s)

Single Motor, 10:1 Gearing Dual Motors, 2:1 Gearing

Figure 76: Displacer profiles at reduced operating speed with dummy load

Figure 77 shows what the displacer motion would look like for the actual load of the displacer (the calculations used a higher than actual value for inertia to allow for the effects of mechanical friction) when driven by the two motors at 2:1 gearing. The three lines represent different operating speeds, showing that at slower speeds it is possible to get a very good approximation to the ideal discontinuous motion profile.

Experimental Data Motor Control System

Time (s)

Displacer Motion with Actual Load

подпись: displacer motion with actual load

^—2 Hz —1.5 Hz 1 Hz

Figure 77: Predicted motion profiles with the actual displacer load at different speeds

Actual Performance

To compare the results for predicted performance with real-world performance a new setup was introduced using the limit switches and an optical encoder as pictured in Figure 78. The optical encoder consist of a disc with 1000 slots in it, such that when it is rotated through a light source with a detector on the other side, a square wave output pattern is generated and each pulse represents 360/1000° of rotation. Using a Cleverscope© USB oscilloscope the output from the encoder was recorded and saved as a text file, where it was subsequently copied into a spreadsheet and used to produce the graphs in Figure 79 and Figure 80.

Experimental Data Motor Control System

Figure 78: Setup for testing limit switch operation

Due to the layout of the limit switches and encoder it was impossible to do these tests with the dummy load of the flywheel in place. However this does not affect the results as it has already been determined what maximum acceleration can be used and this value has been used throughout these tests. Figure 79 shows the motion profile of the displacer, as measured, at an operation speed of 1 Hz. The step pulses in this setup come from a signal generator operating at twice the engine frequency, so 2 Hz in this case. At this speed the motion profile is a good approximation to the ideal motion.

Experimental Data Motor Control System

Figure 79: Plotted graph of actual motion vs. time taken from optical encoder

Figure 80 shows the motion profile of the displacer again, this time operating at twice the speed, which is the maximum engine operating speed of 2 Hz. The blue line in this graph also shows position drift that occurs over time due to open loop operation. If left unchecked this would have dire consequences. However the limit switches do their job as shown by the red line where at a certain point past the desired motion limit they are struck, stopping motion and resetting the origin point.

Operation At 2 Hz With and Without Limit Switches

Experimental Data Motor Control System

No limit switches With limit switches

Figure 80: Plotted graph of actual motion vs. time with and without limit switches

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