Yaskawa SMC–4000 - Manual (Page 30)

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SMC–4000 User Manual
Operation of Closed-Loop Systems
To understand the operation of a servo system, we may compare it to a familiar closed-loop operation,
adjusting the water temperature in the shower. One control objective is to keep the temperature at a
comfortable level, say 90 degrees F. To achieve that, our skin serves as a temperature sensor and reports to
the brain (controller). The brain compares the actual temperature, which is called the feedback signal, with
the desired level of 90 degrees F. The difference between the two levels is called the error signal. If the
feedback temperature is too low, the error is positive, and it triggers an action which raises the water
temperature until the temperature error is reduced sufficiently.
The closing of the servo loop is very similar. Suppose that we want the motor position to be at 90 degrees.
A position sensor, often an encoder, measures the motor position and the position feedback is sent to the
controller. Like the brain, the controller determines the position error, which is the difference between the
commanded position of 90 degrees and the position feedback. The controller then outputs a signal that is
proportional to the position error. This signal produces a proportional current in the motor, which causes a
motion until the error is reduced. Once the error becomes small, the resulting current will be too small to
overcome the friction, causing the motor to stop.
The analogy between adjusting the water temperature and closing the position loop carries further. We
have all learned 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 that 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 between +10 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.