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, ωc, Figures 4 and 5.
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Impact on performance
Integrators enable a servo system to closely follow the intended motion profile. Table 1 shows that a Type 0 position servo has a position error at rest. However, most position servo applications require zero error at final position, so a Type 0 servo would be generally unsatisfactory.
By contrast, a Type 1 servo has zero position error at rest, because it has one position integrator that integrates any position error at rest until the error is driven to zero.
A Type 2 servo offers the fewest position errors with its two integrators, but each integrator has a 90-deg phase lag causing a 180-deg lag around the full loop with both integrators. Therefore, steps must be taken to accommodate this phase lag. To do this, the typical velocity loop inside the position loop is replaced with a single position loop, and the servo amplifier operates simply as a current amplifier rather than as a velocity controller that is used in a Type 1 servo.
A position controller has two basic functions:
• Generate the position trajectory that includes accelerations, velocities, deceerations, and distances, for either a single move or a sequence of moves.
• Close the position loop. This action determines the difference between the position command and the position feedback (at the summing junction, Figure 2). It then applies frequency-response equalization — and other signals if necessary — to this difference, and converts the resultant to an analog voltage that represents the manipulated variable applied to the amplifier. In the velocity mode of control, the manipulated variable (M) is the velocity command. In the torque mode, the manipulated variable is the torque command.
In the velocity mode (Type 1 system), adjustments are made in the amplifier to provide the required frequency-response equalization that will optimize the performance of the velocity loop. Note: When the velocity mode is used, all the frequency response equalization must be done in the amplifier. Attempting to correct for frequency response in the position controller will diminish the system response.
Although the basic strategy for loop closures applies to both modes of control — velocity and torque — position controllers used in the torque mode (Type 2 systems) must have some additional features. In these systems — which omit the velocity loop — the position controller must then factor into its control law a means for monitoring and regulating velocity. In essence, the position controller estimates the velocity based on position feedback. Because of these additional responsibilities, the controller must have an update rate approximately 10 times faster than that required for Type 0 and Type 1 systems.
Understanding that adjusting torquemode controller gains and filter parameters can be challenging, manufacturers of these products typically offer helpful software that either automatically tunes the position loop based on the required performance criteria, or assists in setting the various parameters. Some setup systems also display and plot performance indicators so system performance can be monitored and finely tuned.
Making the selection
Although it is tempting to always select the more versatile Type 2 servo, doing so may be counterproductive. With the increase in adaptability goes an increase in setup complexity. Thus, making the optimum design again involves having meaningful discussions with your supplier, then selecting the best unit for the application. Overspecifying can be just as costly as underspecifying.
Gordon Gorman is an application engineer with Custom Servo Motors, Eden Prairie, Minn., a subsidiary of MTS Systems Corp.
output (C) and the reference (R) is