Servo Motor Drives
How does the DC Servo Motor Produce Torque?
Understanding the operation of a high performance dc servo system is an excellent place to begin before we proceed with a discussion of the ac servo system. The control structure for a dc servo system is identical to the ac servo system and the principle of torque production in a dc servo motor will be used to draw the close parallel to torque production in the ac servo motor.
Cascade Control Structure
The most common structure of a high performance dc servo system is shown in Figure 1. There is virtually universal agreement that the cascaded control structure is the most effective approach to high performance servo systems. The cascade control structure includes an innermost current (or torque) regulator, a speed regulator around t he current (or torque) regulator, and an outermost position regulator around the speed regulator. The sequence of position, speed, and current (torque) is natural as it matches the structure of the process to be controlled. Position is the integral of speed while speed is proportional to the integral of torque. The 4 quadrant power supply just means that the power converter can handle operation of the motor for all combinations of torque (current) and speed (voltage).
The cascade control structure will operate properly only if the bandwidth of the various regulators have the correct relationship. Bandwidth is the range of frequencies over which the controlled quantity tracks and responds to the command signal . In the cascade control, the current regulator has the highest bandwidth, then the speed regulator, and finally the position regulator has the lowest bandwidth. Therefore, the system is properly adjusted beginning with the innermost current regulator and working outward to the position regulator. The cascade control structure also has the benefit of easily limiting each variable by just limiting the commanded value for that variable.
Torque Production with a DC Servo Motor
Understanding the principle of torque production with a dc servo motor (brush-type servo motor) is an excellent foundation for the later discussi on of torque production with an ac servo motor (brushless servo motor). Please refer to the representation of a dc servo motor with a mechanical commutator as shown in Figure 2.
The magnetic field created by the permanent magnet s is fixed in space and is represented by the vector labeled Magnetic Field Vector. A torque is produced by the interaction of the magnetic field and the current-carrying conductors. The torque is a maximum value when the magnetic field vector is perpendicular to the Armature Current Vector. The magnitude of the torque \(T\) is described by the equation: \[T = K \cdot B \cdot I_A \cdot sin \theta \] where \(K\) is a constant determined by the specific motor design, \(B\) is the magnetic flux density, \(I_A\) is the armature current and \(\theta\) is the angle between the two vectors (the torque angle).
The motor torque produced by the interaction of the current-carrying conductors in the magnetic field will cause rotation of the rotor until the torque angle is zero degrees and further motion would not be possible. The dc servo motor eliminates this condition by using a mechanical commutator on the rotor. The commutator causes the current in each conductor to be progressively reversed as the conductor connected to a commutator bar passes beneath the brushes. The physical location of the brushes in a dc servo motor is such that the torque angle is 90 degrees for both directions of rotation. The result is torque generation that is proportional to armature current.
The classic equations that describe the dc servo motor are as follows: \[ T = K_t \cdot I_A \\ U = K_e \cdot \omega_m \] where \(K_t\) is the torque constant, \(K_e\) is the voltage constant, \(U\) is the back electro-motive force, and \(\omega_m\) is the motor speed.
The speed voltage \(U\) is created by the armature conductors moving through the constant magnetic field. \(U\) is referred to as BEMF (back electro-motive force) or CEMF (counter electromotive force) because the polarity is such that it will produce armature current that will interact with the magnetic field in such a way as to oppose motion.
The complete block diagram for the dc servo motor including the armature resistance and inductance is shown below in Figure 3. Now we can see how the torque of a dc servo motor can be easily adjusted by accurately and rapidly controlling the armature current.
Unfortunately, while the control of torque with the dc servo motor is very straightforward, the mechanical commutator introduces many limitations. Some of these limitations include:
- periodic maintenance due to brush wear and brush replacement
- RFI (radio frequency interference) caused by brush arcing
- voltage (speed) and current (torque) limits caused by the mechanical commutation process
- higher rotor inertia due to armature windings and commutator located on the rotor
- a poor thermal situation due to I2R losses in the armature windings on the rotor
- and the cost of the commutator system which needs to be very precise.
The ac servo system with an electronic commutator was developed to eliminate the limitations of the dc servo motor’s mechanical commutator.
How does the AC Servo Motor Produce Torque?
History of Brushless Servo Systems
The permanent magnet dc servo system or brush-type servo has served as the industry workhorse for many decades. While it is straightforward to control torque with a permanent magnet dc servo motor, the mechanical commutator introduces many serious limitations as listed in the previous section. The brushless servo system was developed to eliminate the limitations imposed by the mechanical commutator of a dc servo system
The first implementation of a brushless servo system used three-phase permanent magnet motors and square-wave or rectangular shaped currents. The back EMF waveform of the brushless motors ranged from sinusoidal to trapezoidal. The basic idea was to emulate the brush-type dc servo motor by electronically “commutating” the current from one pair of motor windings to another. Completing the analogy with a brush-type servo system, the motor-mounted feedback devices for a velocity controlled brushless servo system included a commutation encoder and brushless tachometer. The commutation encoder provided the position signals used to transition the current electronically from one pair of windings to another. The analogy to the dc servo system resulted in names for these early brushless servo systems such as brushless dc servo, ECM (electronically commutated motor), six-step servo, and trapezoidal brushless servo.
With careful design, these early brushless servo systems had good performance and they demonstrated the possibility for replacing the brush-type servo motor with a brushless servo motor. However, the design challenges and extra cost of these early brushless servo systems limited application to larger power levels and situations where the extra cost could be justified. This early type of brushless servo is rarely used today in high performance servo systems
Fortunately, the analogy to a dc servo system can also be extended to sinusoidal current excitation of a permanent magnet motor with sinusoidal back EMF. This technology is commonly referred to as field-oriented or vector control. Compared to the first generation of brushless servo systems with square-wave currents, a brushless servo system with sinusoidal back EMF and sinusoidal current is much more practical to manufacture and inherently has much smoother torque production due to the gradual commutation process. This type of brushless servo system is commonly referred to as an ac servo, PM (permanent magnet) ac servo, or sinusoidal brushless servo. For the remainder of this text, we will refer to this state-of-the-art brushless servo system as an ac servo system.
The field-oriented or vector control can also be extended to ac induction motors. Variable speed drives (VSDs) with this technology are referred to as vector drives. Vector drives can be applied as servo drives but the induction motors do not have the performance of the permanent magnet ac servo motors due to higher inertia and larger size. However, vector drives are adequate for some servo applications (particularly larger power applications where permanent magnet ac servo systems are not readily available). The details of vector control for ac induction motors will not be discussed further in this text.
Torque Production with an AC Servo Motor
The best way to understand the principle behind the ac servo system is to develop an analogy to the dc servo system. As discussed earlier, the dc servo motor has a magnetic field that is fixed in space and the mechanical commutator causes the armature current vector to be perpendicular to the field vector at any motor speed or position. The torque produced by the dc servo motor is easily adjusted by controlling the armature current level. As we will soon see, we have an analogous method for controlling the torque of an ac servo motor using vector or field-oriented control.
Let’s start with the magnetic field of the ac servo motor. Figure 4 shows a simple representation of an ac servo motor with a permanent magnet rotor and three-phase stator where the windings are spaced by 120 degrees. The magnetic field vector established by the permanent magnets is labeled B. Unlike the dc servo motor where the permanent magnets are stationary, the magnets of the ac servo motor move as they are mounted on the rotor. The challenge of the field-oriented control strategy is to generate the three-phase stator currents in such a way as to keep the composite current vector perpendicular to the magnetic field vector at all times.
Now let’s review the generation of the composite current vector using Figure 5. The three-phase stator currents are represented as three sine waves that are displaced in space by 120 degrees with axes labeled as U, V, and W. As examples, the composite current vector is developed for angles of 60 and 90 degrees. Notice for every angle that the composite current vector \(I_{dq}\) has a magnitude equal to the amplitude of the phase currents and has an angular position equal to the angle \(\delta\).
Let’s stop and review. We have a fixed amplitude magnetic field vector created by the permanent magnets that rotates synchronously with the rotor of the motor. We also have a composite current vector that rotates at the angular frequency of the phase currents and has an amplitude that is proportional to the peak value of the sinusoidal phase currents. Maybe you can see that we have our answer on how to simply control the torque of the ac servo motor.
Let the angle between the rotor field and stator current be called \(\delta\) and let \(\omega\) be the angular frequency of the sinusoidal phase currents. Then, we just establish \(\delta=90^{\circ}\) so that the current vector \(I_q\)is perpendicular to the magnetic field vector. In practice, this is accomplished by physically orienting the rotor position sensor (usually an encoder or a resolver) so that the composite current vector is perpendicular to the magnetic field vector. Actually, the motor BEMF signal is easier to measure and is uniquely related to the magnetic field vector so the position feedback device is oriented to the BEMF signals during the manufacturing process. In this way, no matter what motion the rotor might make, the current vector will always be perpendicular to the magnetic field vector. We now have an ac servo system where the torque can be controlled just like the dc servo system and where the ac servo motor “looks” just like the dc servo motor to the speed and position regulators. Let’s draw a picture of the vector control for an ac servo motor as shown in Figure 6.
AC Servo System
- Permanent magnets on the rotor create a field vector that rotates synchronously with the rotor of the motor
- Composite current vector is located perpendicular to the field vector at all times by locking the angular frequency of the three phase stator currents to the properly defined rotor angle \(\delta\)
- Torque is then directly proportional to the amplitude of the three-phase sinusoidal currents.\[T=K_t I_{q}\]
- Field vector is fixed in space by the stationary permanent magnets
- Current vector is located perpendicular to the field vector by proper location of the brushes on the commutator
- Torque is then directly proportional to the armature current.\[T=K_t I_A\]
Overview of the AC Servo System
Introduction
The purpose of this section is to review some of the theory behind the major components of an ac servo system. Figure 7 repeats the block diagram of the ac servo system and highlights the five areas of discussion. The digital ac servo system is typically available with three modes of operation:
- Torque Control Mode
Analog input is the current command signal which we know from earlier discussions is proportional to motor torque. Tuning is required and some adjustment may be required to scale the analog input to current or torque. - Velocity Control Mode
Analog input is the velocity command. The velocity regulator is tuned for the motor and load. - Position Control Mode
Step and Direction (stepper emulation) is the position command. Both the velocity regulator and the position regulator must be adjusted for a specific motor and load.
The AC Servo Motor
The permanent magnet ac servo motor has a very straight-forward and rugged construction. The stator has three symmetrical windings, which are internally connected in a wye configuration. The neutral connection is not brought outside the motor so only three power wires are available from the motor. Compared to the dc servo motor, the construction of the ac servo motor is thermally more effective because almost all of the losses are in the stator where they can be more easily routed to the outside ambient.
The rotor contains the permanent magnets, which can be mounted in different ways depending on a specific supplier’s technology. The permanent magnet material ranges from low cost ceramic (ferrite) to the more expensive rare-earth materials such as samarium cobalt or neodymium iron boron (“neo”). Most recent ac servo motor designs use “neo” as a good compromise between magnetic properties, availability, and cost. The rotor also includes a rotary position sensor. The multi-purpose position sensor is used for commutation (or generation of the sinusoidal current commands), velocity feedback, and position feedback
The block diagram of an ac servo motor is shown in Figure 8. It is very similar to the block diagram of the dc servo motor in Figure 3 except that the voltage and current values are sinusoidal. The block diagram in Figure 8 is very useful in developing an understanding of the relationship between voltage and current in the ac servo motor.
The vector control of the ac servo motor allows the phase current to be kept in phase with the BEMF at all times and by controlling the amplitude of the phase current we can adjust the level of motor torque. The voltage relationships and torque-speed curve for an ac servo system are shown in Figure 9 as developed from the ac servo motor block diagram in Figure 8
The voltage and current relationships are important because they determine the torque-speed operating boundary for the ac servo system. With vector control, the torque is adjusted by the level of phase current and by keeping the phase current in phase with the BEMF. The terminal voltage required to create the necessary phase current can be determined as shown in Figure 9. The current controlled power converter has a maximum available voltage as determined by the ac supply. When the maximum available terminal voltage has been reached due to requested torque (current) or speed, then the phase current can no longer be properly controlled and we no longer have the proper relationship between torque and current.
The following equations can be used to calculate the ideal maximum voltage available from the power converter. The actual voltage will be lower due to various voltage drops in the system.
- Maximum DC link voltage \[ V_{DC} = \text{ DC Bus Voltage} = \sqrt{2} \cdot V_{AC} \text{( AC Supply Voltage)} \\ \] Example: \[ V_{DC} = 325 V(dc) = \sqrt{2} \cdot 230V \text{( r.m.s. line to line)} \]
- Maximum \(V_{phase}\) = Maximum available line to neutral voltage: \[ V_{phase} = \frac{V_{DC}}{ \sqrt{3} \sqrt{2}}\\ \] Example: \[ V_{phase} = 133 V^{rms} = \frac{325}{ \sqrt{3} \sqrt{2}} \]
The Position Sensor
The ac servo motor has a rotary position sensor, which is mounted on the non-drive end of the motor. As we have seen in Figure 6, the position sensor is used for the electronic commutation of current, speed feedback, and position feedback. The most common position sensor used with ac servo motors is the optical incremental encoder. In special cases, where homing the load on power-up is not acceptable, a more costly multi-turn absolute position feedback device is used instead of the incremental encoder
Today’s ac servo systems are almost all digital. Optical incremental encoders which provide digital information are easily interfaced to digital servo drives where they offer high resolution and accuracy at an attractive cost. The basic operation of a “wire saving” incremental encoder is shown in Figure 10. The low resolution absolute position start-up signals are only necessary during power-up to initialize the rotor angle inside the digital servo drive. The high resolution data tracks and marker pulse (C signal) are used after power-up and during normal operation of the system. By using the “wire-saving” design, the same 6 wires can be used for both start-up and normal operation which minimizes the cost and diameter of the cable running between the drive and motor. Including the dc supply wires, the “wire-saving” encoder only requires 8 total wires. However, in practice, small gauge wire is used so it is common to double or even triple-up on the supply lines in order to minimize voltage drop over longer cable lengths. As an alternative, some drives use a pair of voltage sensing lines to measure supply voltage at the encoder and then adjust the supply voltage at the drive to maintain the proper voltage at the encoder.
A representation of the signals from the incremental optical encoder is shown in Figure 11. For simplicity, the signals are shown without the complement signals from the line drivers. However, in practice, differential feedback signals are essential to eliminate noise problems and to facilitate long cable lengths.
The encoder is attached to the ac servo motor in a very particular and precise way during the assembly of the motor. From earlier discussions, the rotor angle must be defined so that the composite current vector is kept perpendicular to the magnetic field at all times. The start-up signals provide low resolution absolute position information to initialize the rotor angle in the servo drive. The resolution of the start-up signals provide for ± 30 degree accuracy of the torque angle. As torque is proportional to the sine of the torque angle, we have at least 86% of maximum torque available to move the load up to one mechanical revolution until we pick-up the C signal or marker pulse. After we detect the marker pulse, the torque angle is set to the exact value necessary for a 90 degree torque angle.
The marker pulse has a unique position relative to the start-up signals which is determined by the manufacture of the encoder and which is specified by the supplier of the servo system. The marker pulse also has a unique relationship to the motor BEMF signal and is precisely aligned during the installation of the encoder onto the motor. The accuracy of the marker pulse to the motor BEMF signal is usually at least ± 2 mechanical degrees which provides more than 99% of maximum torque for 4, 6, and 8 pole motors.
Finally, the A and B data signals typically provide 2000 cycles per mechanical revolution. The servo drive encoder interface circuit is designed to detect all of the edge transitions for the data signals so the 2000 “line” encoder provides 8000 counts or pulses per revolution (ppr).
The Current Controlled Power Converter
As discussed earlier, the ac servo motor produces torque which is proportional to the amplitude of the composite current vector. As you can imagine, the ac servo drive must produce current accurately and with high response. This extremely important task is the work of the current controlled power converter as shown in Figure 12.
The system is supplied by the ac mains which typically is required to be single phase or three phase voltage at 230 Vrms (+10%/-15%) and 50 Hz. Sometimes the ac supply is buffered by a transformer in order to provide the correct voltage level. The primary attribute of the ac supply is that it needs to maintain the required voltage level even as it is loaded by the servo drive(s) or other items attached to the supply.
The diode rectifier converts the ac input into a dc voltage, which is called the “dc bus”. Included with the diode rectifier is a circuit to control the inrush current(s) during power-up. Without the “soft start” or “soft charge” circuit there would be very large inrush currents to charge the dc bus capacitor. After initial power-up, the rectifier circuit is free to provide the necessary energy to the servo system as required.
The dc bus capacitor has a large value, which serves two purposes. One purpose is to act as a large filter so that a smooth dc bus voltage is available to the inverter. The second purpose is to help absorb energy during regeneration or braking of the motor and load. While the diode rectifier can supply power during motoring or driving, it cannot return power to the ac supply during braking. The regeneration energy is absorbed by the dc bus capacitor until it charges to a maximum allowable voltage and then the regeneration circuit “dumps” excess energy in the regeneration resistor where it is eliminated in the form of heat. Most ac servo drives include a small built-in regeneration resistor while having the provision for adding an external resistor with a much larger wattage.
The inverter is designed with power switches that are turned “on” or “off”. These power switches can be bipolar transistors or power FETs but most ac servo drives today use a newer switch referred to as an IGBT (insulated-gate bipolar transistor). The IGBT combines the rugged output of the bipolar transistor with the gate drive and fast turn-off time of the power FET. The inverter topology, with the six switches and the “flyback” diodes, provides four quadrant operation of the ac servo motor by allowing energy to flow to and from the motor.
Let’s take a look at the current controller design for one of the three phases. The other two phases operate in an identical fashion.
- The desired current or current command is IU and it can be limited to a user defined value (up to a maximum as determined by design limits). The current command is compared to the current feedback to produce a current error. As you can imagine, the current sensors must be very accurate and responsive devices, as they must absolutely produce a faithful reproduction of actual current.
- The current error is processed by the current regulator to produce the voltage command. The current regulator has a high-gain to minimize the current error over the operating range of the system. The voltage command is compared to a triangle voltage to generate the PWM (pulsewidth-modulated) signals that command the power switches to turn-on and turn-off. The switching frequency of the PWM inverter is usually in the range of 5 to 20 kHz in order to support the high current loop bandwidth and to minimize the audible noise and level of current ripple. The –3dB bandwidth of the current loop is usually well over 1,000 Hertz
- The power switches are not perfect and they do take some time (typically a few µsecs) to turnoff after receiving the command to turn-off. Unfortunately, the switches respond to the turn-on signal more rapidly so the “on” and “off” commands are processed by some special circuitry to prevent the upper and lower switches from simultaneously conducting current. Such a condition is referred to as a “shoot-through” and it is as bad as it sounds. The “lock-out” circuitry introduces a small delay in the turn-on signal to prevent shoot-through conditions.
- Now for the best news of all. The current controller is the domain of the ac servo system manufacturer and requires no user adjustment at all! The operation of the current controller is absolutely critical to the performance of the servo system and the necessary adjustments only involve knowledge of the servo drive design and the motor design. Therefore, the servo system manufacturer has all the information necessary to provide for the optimum set-up with a minimum of user intervention. At most, the user will be asked to supply the drive with the motor model number or similar identifier.
Finally, a dynamic brake (DB) circuit is shown between the inverter and the ac servo motor. The DB is used in the event of a servo drive fault condition to help brake the motor. Often, the DB circuit is included inside the servo drive which is very convenient. The DB circuit uses contactors to disconnect the motor from the inverter and to connect the motor windings together through resistors. If the motor is rotating, the BEMF causes current to flow in such a way as to retard rotation or to dynamically brake the motor.
The Velocity Regulator
Let’s begin with a block diagram of the velocity controlled servo system as shown in Figure 13. The most common choice for the velocity regulator is a PI controller (proportional plus integral controller). The proportional gain \(K_{vp}\) and the integral gain \(K_{vi}\) are adjusted to achieve the desired response. The well-damped current controller can be approximated at the lower frequencies as a first order lag. Recall from the previous section that the current controller is set-up by the servo system supplier and no adjustments are required by the user. The load and motor are modeled as a pure inertia but can be complicated as required to model any actual load. Also, notice that the velocity controller has two inputs to consider: the speed command and the often overlooked load or disturbance torque.
The \(K_{vp}\) term is increased to achieve faster response but unfortunately also has the effect of simultaneously slowing down the response of the integrator. The \(K_{vi}\) term is raised to increase the response of the integrator (reduce the integrator time constant). This unfortunate interaction is better seen by rearranging the block diagram of the PI regulator into a form equal to \[ K_{vp} (1 + 1/Tvis) \] where the integrator time constant is \[ T_{vi} = \frac{K_{vp}}{K_{vi}} \] The use of \(K_{vp}\) and \(T_{vi}\) makes it intuitive to tune the PI controller. The proportional gain and the integrator time constant can be independently adjusted without the interaction on each other. Figure 14 shows the revised block diagram of the velocity regulator with independent adjustment of gain and integrator time constant where we have also assumed perfect current control for additional simplicity.
In practice, the velocity regulator is tuned or adjusted to result in a well-behaved control system as defined by stability, steady-state accuracy, transient response, and frequency response. Let’s discuss these design objectives in some more detail:
- Stability
- Steady-State Accuracy
- Transient Response
- Frequency Response
The most common method of manually tuning the velocity controller is to observe the speed response to a small-signal step change in the speed command. For best results, this must be done with the motor connected to the actual mechanical load. Small-signal means that the current command is not reaching a limit condition during the tuning process. The desired response is one that reaches the setpoint with acceptable risetime, overshoot, and settling time. The objective is to find values for \(K_{vp}\) and \(T_{vi}\) that minimize risetime, overshoot, and settling time while still allowing for some safety margin in the stable operation. It is not good practice to tune the system with gain values that leave the system on the verge of instability. Figure 15 shows some examples of velocity responses to small-signal step changes in the velocity command as we make various changes to \(K_{vp}\) and \(T_{vi}\).
Steady-State Accuracy
The well-tuned servo system should not have any steady-state error for a step change in the velocity command or load torque. The closed loop transfer functions developed from Figure 13 are shown below (where we have also assumed an ideal current controller):
\[ \frac{\omega}{\omega^*}= \frac{\frac{K_{vp}}{J}(s+\frac{K_{vi}}{K_{vp}})} {s^2 + \frac{K_{vp}}{J}s + \frac{K_{vi}}{J}} \] \[ \frac{\omega}{T_{Load}}= \frac{\frac{1}{J}s} {s^2 + \frac{K_{vp}}{J}s + \frac{K_{vi}}{J}} \] \[ \frac{\delta}{T_{Load}}= \frac{\frac{1}{J}} {s^2 + \frac{K_{vp}}{J}s + \frac{K_{vi}}{J}} \]Using the final value theorem, the steady-state error for step-command inputs can be determined. The first two equations show that the velocity error is zero for a step change in the velocity command or the torque disturbance. However, the last equation shows that there is a steadystate position error for a step change in load torque where d/TLOAD = 1/Kvi. \[ \frac{\delta}{T_{Load}}=\frac{1}{K_{vi}} \] The static position error or “stiffness” of the velocity loop is improved with higher \(K_{vi}\) values or a smaller value integration time constant. Do not be concerned at this time with the static position error as we will show in the next section that when the position loop is closed, the static position error for a step change in load torque will also be zero. So, we can conclude that the PI controller as a velocity regulator provides excellent attributes for steady-state accuracy.
Transient Response
The transient response is analyzed in much the same manner as the relative stability. We are looking for a response to a step change in command or load torque that has acceptable rise time, overshoot, and settling time characteristics. The closed-loop response of a well-tuned control loop often has characteristics that are dominated by a pair of underdamped complex poles. For this case, a useful rule of thumb that relates the rise time and closed loop bandwidth is as follows: \[ (Rise\:Time) \cdot (Closed \:Loop\; Bandwidth [Hertz]) \cong 0.45 \]
Once again, the objective for the tuning is to provide just enough response and stiffness without leaving the system on the verge of instability as in Figure 16. We want a safety margin to allow for any changes in a particular system and to provide standard tuning values that can be reapplied on multiple systems.
Frequency Response
As we discussed earlier, the cascade control system works properly when the bandwidth of the control loops have the proper relationship to one another. The inner current loop must have the highest bandwidth and the velocity loop must have a bandwidth that is higher than the position regulator. In fact, when the outer loop is position, it has been shown that the relevant velocity loop bandwidth is the “useful” bandwidth which is defined as the frequency where the actual velocity lags a sinusoidal commanded velocity by 45 degrees (as opposed to the more common definition of bandwidth as the frequency where the amplitude of the controlled quantity has dropped –3 dB). The rule of thumb is that the useful bandwidth of the velocity loop must be at least 3 times the required position loop bandwidth. This avoids overshooting in the position loop
Unfortunately, actual loads that are connected to the servo system seldom behave like an ideal inertia. The actual loads can have friction, damping, compliance, backlash, variable inertia, and other possible non-linearities. This is why the set-up of the ac servo system is best when attached to the actual load. The better ac servo systems also have additional features that help the user in dealing with the variety of possible load conditions. Figure 17 shows the block diagram of a velocity regulator with some of the additional features that many digital ac servo systems offer to help deal with difficult load conditions.
Many digital ac servo drives also have an auto-tune mode that estimates the value of load inertia and initially sets the tuning parameters to reasonable values for user specified targets such as low, medium or high response. The auto-tune values usually provide a stable system that is often sufficient for the application or at least serves as a starting point for fine-tuning by the user.
Let’s take a look at the extra functions provided in Figure 17.
The optional acceleration/deceleration (Acc/Dec) function is a programmable slew rate limit if the speed command were to change too abruptly. This is a very common feature for adjustable speed drives as the only means of acceleration and deceleration limiting. This feature is not usually used when the velocity servo is connected to an external position controller because the position controller already has acceleration and deceleration limits.
The optional low pass filter for the speed command (VLPF) is adjusted by the user. Be aware that the low pass filter will introduce additional phase shift into the position controller as the filter frequency is reduced. The resolution of the velocity command is high so the low pass filter should not be necessary unless there is an unusual amount of noise or jitter on the speed command signal.
The optional low pass filter for the current command (ILPF) is programmed by the user and can be very useful when the gain of the velocity regulator is high. Any jitter in the velocity error signal is multiplied by the high gain of the velocity regulator to cause high frequency oscillations in the current command signal. The result is audible noise, which can be eliminated or reduced by filtering the current command signal. However, once again, do not lower the frequency of this filter more than necessary as it will introduce additional phase shift into the velocity controller which reduces stability.
The final optional feature is the notch filter. The notch filter is used when the resonant frequency of the motor and load system is amplified by the servo system. Figure 18 shows a simple model of the motor inertia and load inertia which are connected together by a shaft with a stiffness coefficient labeled \(K_{SHAFT}\) [Torque/Radian]. The center frequency of the notch filter can be programmed to cancel or minimize the gain at the resonant frequency.
We have reviewed many aspects of the velocity regulator for the high performance ac servo system. However, the best way to become proficient at tuning the PI controller is to spend time tuning actual systems while observing the effect of changing \(K_{vp}\) and \(T_{vi}\). Tuning the PI regulator is a skill that is learned somewhat like riding a bike. While the concepts discussed here are important to understand, to really master the skill, you must spend hands-on time tuning the PI controller under various load conditions. With a little theory and a lot of experience, you will be able to intuitively tune the PI controller under the most demanding load conditions.
The Position Regulator
Position control applications fall into two basic categories: contouring and point-to-point.
In general, contouring applications are focused on following a path. Contouring applications require the actual position to follow the commanded position in a very predictable manner and to have high stiffness to reject the effect of any load torque disturbances. Point-to-point applications are not usually concerned with path control but are concerned with move time, settling time, and the velocity profile.
Independent of the positioning application, the basic position controller is shown in Figure 19. The velocity controller is modeled as a first order lag where the time constant is determined by the useful bandwidth.
Understanding the operation of the position regulator with only proportional gain is a good first step. The gain of the open loop frequency response for the system in Figure 19 crosses 0 dB at a value equal to \(K\). Therefore, the bandwidth of the position loop can be expressed as follows: \[ K = 16.66 [rad/sec] = 2.65 [Hz] = 1 [inch/min/mil] = 1 [meter/min/mm] = [velocity/position] error \]
The actual position controller contained within the ac servo drive will have a gain KP that has useful units such as rad/sec. This is very helpful when tuning the position loop.
Now, let’s take a look at the static stiffness of the simple position loop. From Figure 19, we can see that the steady-state position will equal the commanded position due to the effect of the velocity integration into position. The effect of a step change in load torque is a little more difficult to analyze. However, referring to Figure 20, we can laboriously develop the transfer function between position and load torque as having the form: \[ \theta = \frac{\frac{1}{J}} {s^2+\frac{1}{J}G_c (s+K_p)} T_{Load} \]
If the velocity controller \(G_c\) is a PI controller and \(G_p\) the motor, then we can demonstrate using the final value theorem that there is no position error in the steady-state condition when there is a step change in load torque. This is another good feature of the PI controller in the velocity loop.
The actual position regulator can be more complicated than a simple proportional gain. A more general position controller is shown in Figure 21
Let’s quickly review the features of the general position regulator shown in Figure 21.
The proportional gain remains the most important term. The proportional gain will generate a velocity command that is proportional to position error. In other words, with only a proportional gain, motion will occur only if there is a position error. In fact, the position error will increase with increasing speed. The dynamic position error or following error can only be reduced by increasing the proportional gain. However, there is a limit on position loop gain (determined by the useful bandwidth of the velocity loop) and if the gain is increased too much then the actual position will begin to overshoot the commanded position which is normally not acceptable. However, recall that the static position error is zero if the position command is not changing.
The feedforward gain is used to reduce the following error. The feedforward gain generates a velocity command signal that is proportional to the derivative of the position command. Ideally, 100% feedforward would generate the exact velocity command without the need for a position error. However, in practice, the system is not ideal and it is prudent to use less than 100% feedforward since too much feedforward will cause the actual position to go farther than the commanded position. In any event, the use of feedforward will significantly reduce the following error even though the proportional gain is at a level for proper stability as shown in Figure 22.
