BME355 Lab Listing
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Control Systems


Preparation

Lab Outline

Procedure

Learning more

GOALS

Understand the behavior of a simple feedback control system including the role of gain and the effect of noise
Demonstrate the basic properties of feedback control systems using the eye/hand motor control system
Identify limitations of the linear, shift-invariant model of a physiological system
Characterize system frequency response using a Bode plot

Preparation

A simple and powerful approach to controlling the behavior of a system is to adjust an input parameter according to the system's output.  This is known as feedback control; it is used throughout biomedical engineering in areas such as drug delivery, ventilation, arrhythmias, etc. and plays a role in virtually every physiological system.

To discuss control systems, we must first define several key terms:
  • Input: Parameter or stimulus applied to a control system from an external source, usually in order to produce a specified response from the system.
  • Output: The actual response obtained from the system.
  • Feedback: That portion of the output of a system that is returned to modify the input and thus serve as a performance monitor for the system.
  • Error: The difference between the input stimulus and the output response (feedback).
A very simple example of a feedback control system is the thermostat. The input is the temperature ("set point") that is initially set into the device. Comparison is then made between the input and the ambient temperature ("sensor response"). If the two are different, an error results and an output ("control") is produced that activates a heating or cooling device. The comparator within the thermostat continually samples the ambient temperature, i.e., the feedback, until the error is zero; the output then turns off the heating or cooling device.

A block diagram of a simple feedback control system is shown in this figure:


The output of the system (the "response") is fed back to the input end, and compared to the desired response or set point.  The difference between the set point and the true response is called the error signal.  Assuming that the system output is a monotonic function of its input, the amplified error signal can be used to drive the system output closer to the set point.  Suppose that the system output increases monotonically as a function of its input, and when the input is ideal then the output equals the set point (see the figure below).  If the response is too low, the error signal will be positive.  For a positive gain factor, the input to the system increases, so the response also increases, making it closer to the set point.  If the response is too high, then the error is negative and (assuming positive gain), the system input decreases, and so does the response. In either case, the system output moves toward the set point.


An attractive feature of this scheme is that no detailed knowledge of the system is needed in order to control its output, and in fact, the system can be controlled even if its behavior changes with time (within broad limits).  This includes the effects of noise.

This lab has two parts.  The first part uses a simple temperature control system to illustrate some important effects of feedback gain.  The second part uses your eye/motor system to demonstrate the role of the frequency response of a control system (in this case a physiological system).

The temperature control system includes a Peltier junction, an amplifier, and a temperature sensor.  The Peltier junction is a semiconductor device which acts as a heat pump.  The Peltier effect refers to the absorption or liberation of heat at the junction of two dissimilar conductors whenever current flows through the junction.  If many junctions join two parallel plates, significant thermal power can be pumped from one plate to the other (computer chips are sometimes cooled this way).  The direction of heat flow reverses when the current reverses.  In our device, one side of the Peltier junction is cemented to a heat sink (which stays close to room temperature) and the other is fixed to a small block of aluminum.  Current passing through the Peltier junction therefore raises or lowers the temperature of the aluminum block relative to the room temperature.   (see Thermoelectric Devices for more information)

The power amplifier is necessary to drive the Peltier junction, which requires higher currents (of order 1 Amp) than the computer's I/O board can supply.  A sensor (the AD590) is embedded in the aluminum block to monitor its temperature.  You will program the computer to read the temperature of the block, calculate the difference between the actual and set point temperatures, and apply a feedback signal to the Peltier junction's power amplifier to reduce this temperature difference.

In the motor control study, the computer will display an error function, which you will try to minimize.  This becomes progressively more difficult as the frequency of the command function (the set point, as a function of time) increases.  The frequency range over which you can control the system is predicted by the Bode plot of your impulse response function.

The Bode plot (suggested by Hendrik W. Bode in the 1930's) is a graphical approach for analyzing systems. Bode's method consists of plotting two curves, the log of gain, and phase, as functions of the log of frequency.

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