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The Type (0, 1, or 2) of a closed-loop servo system defines some of the servo components, relates to overall system performance, and defines how other system components should be used. In summary, the Type defines the number of integrations within a control system. But before we jump to that point, let’s cover some basics.

A servo system, which is inherently a closed-loop control system, includes a feedback to ensure that the system output follows the input command with acceptable speed and accuracy. A simple servo system, Figure 1, includes components that are common to all such systems: a summing junction and a plant or actuator, which has a gain of (A). The system input, reference command (R), is the independent variable. The output is the variable output (C). The feedback to the summing junction is tied directly to the output. Therefore, this configuration is described as a fully fed-back servo.

The difference between the reference input (R) and the feedback (C) is an error (E). The relationship between the output (C) and the reference (R) is called the transfer function:

If the gain (A) is 10, then the function, C/R is 0.909, which means that the output tracks the command with an accuracy of 91%. However, if A is 100, the output tracks the command with an accuracy of 99%. Therefore, servo systems generally have adjustable gains to achieve the desired output performance.

A common example of such a servo is a machine tool slide. Here, the controller, a CNC positioning module, gives a reference command that describes the desired position trajectory. The plant includes the amplifier plus the motor and drive train, and the feedback is the axis position transducer. The system in this basic example regularly monitors the difference between the command and the feedback, then it applies appropriate gains and filters to produce a signal to the plant that drives the error to an acceptable value.

However, by today’s standards, machine operation is generally not so simple that a servo shown in Figure 1 alone will deliver the needed results. Therefore, Figure 2 shows a more typical system with intermediate variables, control elements (G₁), plant (G₂), and feedback elements (H). The summing junction along with the control elements are often referred to as the controller. The variables include the reference (R), error signal (E), manipulated variable (M), disturbance (D), and primary feedback signal (B). The transfer for this more typical system is:

Behavior of an integrator

A device with an output that generally relates to an integral of its input is an integrator. An example of an integrator is a simple resistor in series with a capacitor, Figure 3. Following a step change in voltage applied to the network, current flows through the resistor to charge the capacitor. The voltage across the capacitor builds up in exponential fashion. The capacitor voltage relates to the integral of the current flowing through the resistor.

In mathematical terms, the gain of an integrator can be expressed as:

Thus, an integrator changes gain magnitude inversely proportional to frequency, and it causes a 90-deg phase lag at all frequencies. Plus, when the frequency, ω, has the same magnitude as the gain constant, K, the integrator has unity gain (0 dB on the log-log plot). This frequency that produces the unity gain is the cutoff frequency, ω_c, Figures 4 and 5.

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