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Chapter 10 Theory of Operation
DMC-1000
The analogy between adjusting the water temperature and closing the position loop carries further.
We have all learned the hard way, that the hot water faucet should be turned at the "right" rate. If you
turn it too slowly, the temperature response will be slow, causing discomfort. Such a slow reaction is
called overdamped response.
The results may be worse if we turn the faucet too fast. The overreaction results in temperature
oscillations. When the response of the system oscillates, we say that the system is unstable. Clearly,
unstable responses are bad when we want a constant level.
What causes the oscillations? The basic cause for the instability is a combination of delayed reaction
and high gain. In the case of the temperature control, the delay is due to the water flowing in the
pipes. When the human reaction is too strong, the response becomes unstable.
Servo systems also become unstable if their gain is too high. The delay in servo systems is between
the application of the current and its effect on the position. Note that the current must be applied long
enough to cause a significant effect on the velocity, and the velocity change must last long enough to
cause a position change. This delay, when coupled with high gain, causes instability.
This motion controller includes a special filter which is designed to help the stability and accuracy.
Typically, such a filter produces, in addition to the proportional gain, damping and integrator. The
combination of the three functions is referred to as a PID filter.
The filter parameters are represented by the three constants KP, KI and KD, which correspond to the
proportional, integral and derivative term respectively.
The damping element of the filter acts as a predictor, thereby reducing the delay associated with the
motor response.
The integrator function, represented by the parameter KI, improves the system accuracy. With the KI
parameter, the motor does not stop until it reaches the desired position exactly, regardless of the level
of friction or opposing torque.
The integrator also reduces the system stability. Therefore, it can be used only when the loop is stable
and has a high gain.
The output of the filter is applied to a digital-to-analog converter (DAC). The resulting output signal in
the range b10 and -10 Volts is then applied to the amplifier and the motor.
The motor position, whether rotary or linear is measured by a sensor. The resulting signal, called
position feedback, is returned to the controller for closing the loop.
The following section describes the operation in a detailed mathematical form, including modeling,
analysis and design.
System Modeling
The elements of a servo system include the motor, driver, encoder and the controller. These elements
are shown in Fig. 10.4. The mathematical model of the various components is given below.
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