ELEC 243 Lab

Experiment 7.2

Control

Components

Although we usually think of a fan as a device which produces flow, since it has to drive that flow through the constricted air paths inside the equipment it is cooling, our fan must also be capable of producing pressure, i.e. it is also a pump.

Since we now have a device that can produce pressure and a device that can measure pressure, we can combine them to produce a system that regulates pressure i.e. a control system.

In order to build up a pressure we need to confine the output of the fan to a reasonably small volume. To facilitate this we have assembled a pressure control assembly from space-age plastic components. The fan assembly from the previous Experiment conveniently slips into one end of the structure, and the vinyl hose from the pressure sensor fits onto the barbed fitting in the center.

Part 1: System Characterization



Wiring:

 If the connections from Experiments 8.1 and 8.2 are intact, there's no more wiring to do.

Assembly:

 Start the VI. If necessary, reset the Offset value so that the Pressure reads zero when nothing is moving. Slip the fan assembly into the open end of the tee fitting. It should fit snugly, if not wrap a layer of tape around it. Push the end of the vinyl hose (whose other end should be connected to the pressure port of the pressure sensor) onto the barb fitting in the center of the tee. The remaining branch of the tee should be sealed with a rubber stopper. The assembly will vibrate when running, so be sure that it is placed so that it will not fall off of the bench, or else have your lab partner hold it.

Testing:

 Start the VI and turn on the power. Increase the setting of the Motor control slider. As the fan begins to turn, you should get a positive pressure reading, which should increase to a value of about 0.13-0.15 kPa with the control at maximum. If the pressure is negative, take appropriate action to reverse the sign. The easiest fix is to move the tubing to the other port of the pressure sensor.

Characterization:

 Measure and plot pressure vs. motor drive at an appropriate number of points. Repeat the characterization with the rubber stopper removed.

Part 2: Manual Control

Pick a value of pressure between 0.04 kPa and 0.08 kPa and enter this value into the numeric control labeled Set Point (located directly above the motor control slider). Start the VI and adjust the Motor slider until the measured pressure matches this value. Replace (or remove) the rubber stopper and readjust the motor drive until the pressure is correct. Enter a new value of pressure into the Set Point control. Readjust.

This is an example of manual control, similar to the way you control the speed of your car when not using the cruise control. The changing of the set point corresponds to moving between different speed zones and the insertion and removal of the stopper is a form of disturbance. Disturbances are uncontrolled external inputs (e.g. a wind gust) or changes in system parameters (e.g. a hill) which necessitate an adjustment to the controlling input in order to maintain the desired output.

Although a certain amount of enjoyment results from controlling the speed of a car, controlling the speed of the fan gets old in a hurry. This is clearly a process which should be automated. There are two approaches we could try: (a) find the correct value of the controlling input and maintain that value until something changes (as we did with manual control), or (b) switch between two speeds, full on or off, in such a way as to keep the the controlled variable acceptable limits. We'll try approach (b) first, since it's easier.

Part 3: On-Off Control

There's a simple algorithm for on-off (also called bang-bang) control: Determine the maximum allowable error, or hysteresis. Set an upper threshold equal to the desired value plus the hysteresis and a lower threshold equal to the desired value minus the hysteresis. If the actual output value is greater than the upper threshold, turn the drive off. If it is below the lower threshold, turn the drive on.


Setup:

 Select the On-Off tab of the tab control panel.

Testing:

 Start the VI. The pressure should oscillate in a small band around the set point.

Observations:

 Adjust the hysteresis, change the set point, insert and remove the stopper. Observe how the system responds.

Part 4: Proportional Control

In proportional control, the value of the error is multiplied by a constant ($K_p$ ) and used as the input to the driving amplifier. Since this involves feeding a sample of the output back into the input of the system, it is called feedback control. A little thought shows that if a non-zero input is required in order to have a non-zero output (as is in the case with our pressure control system), then the error can never be driven completely to zero (since the input is a multiple of the error).

However, if we integrate the error before feeding it back into the input, then it is possible to have a zero steady-state error. A controller which does this is called an integral controller. As with the proportional controller, there is a parameter $K_i$ , called the integrator gain, which adjusts the amount of integrated error fed back to the input.

An integral controller can achieve zero error, but is sluggish. A proportional controller can respond quickly, but can't achieve zero error. By combining the two, we get a proportional-integral (PI) controller.

\includegraphics[scale=0.500000]{ckt8.3.2.ps}

In the diagram $\frac{1}{s}$ is the Laplace Transform notation for integration, so $\frac{K_i}{s}$ represents $K_i\int_0^tf(\tau)d\tau$ .


Setup:

 Select the Proportional tab of the tab control panel.

Testing:

 Start the VI. The pressure should settle to a value very close to the set point.

Characterization:

 With the default values of $K_p$ and $K_i$ , change the set point (with the VI running) and insert and remove the stopper. Observe how the system responds.

Turn the integrator off and observe how effective proportional control alone is. Try various values of $K_p$ and note how this affects behavior.

Turn the integrator back on and try various combinations of $K_p$ and $K_i$ .