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
PreparationA 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:
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