Observant resolvers

by George Ellis
Senior Scientist
Kollmorgen
Danaher Motion
Radford, Va.

Industrial servosystems often rely on resolvers for accurate feedback. A tracking loop usually converts resolver signals to position data. The conversion process causes phase lag between the actual and measured positions. This phase lag causes instability in the control loop, reducing performance.

One efficient solution to this problem is the use of mathematical constructions called observers. Observers are a well-known way to reduce phase lag caused by sensors. They have several advantages including providing position and velocity feedback with little or no phase lag, and estimations of motor acceleration and torque disturbance. The estimated acceleration is used to reduce problems with mechanical resonance, and torque disturbance feedback improves dynamic stiffness of the control system.

Resolver basics
Resolvers are common position-sensing devices. There are two basic resolver configurations; housed and frameless. Housed resolvers have independent bearings and an output shaft. Frameless resolvers come in two pieces, a rotor and a stator, which mounts to the motor. Resolvers have several advantages over other feedback devices, the most important of which are low cost, rugged construction, and high reliability.

Resolvers are basically multiwinding transformers where the transformer ratio varies with position. The electromagnetic interaction between the rotor and stator provides signals indicative of position. Resolvers have three windings; a reference, a sine feedback, and a cosine feedback. The reference is a fixed sinusoidal signal, typically 4 to 8 V, with a frequency of 4 to 10 kHz. The resolver acts like a rotating transformer with two secondary windings and a single primary, which is the reference signal. The ratio of the reference winding to the two feedback windings varies with the position of the rotor.

Resolver signals get processed, generating a position signal, via resolver-to-digital conversion, or RDC. RDC is usually structured in a tracking or double integrating loop. This loop acts like a filter, reducing the magnitude of high-frequency noise, but also generating lag between the actual position and the RDC output. Phase lag within a control loop reduces stability margins, thus forcing use of lower servo gains. Ultimately, sufficiently large phase lag degrades machine performance.

A model of the RDC shows that the system behaves like a second-order low-pass filter. At low frequencies, the converter generates no significant effects. However, high frequencies experience attenuation and phase lag. This phase lag can cause stability problems such as overshoot and ringing. This forces the reduction of gains, lengthening response times. Drive manufacturers typically try to maximize the compensator gains to raise the effective bandwidth of the RDC which, in turn, minimizes phase lag. However, stability margins and noise combine to limit the bandwidth so the typical RDC has a bandwidth of about 600 Hz.

Electrical noise from sources such as EMI is another problem. It causes random behavior in the control system, corrupts the output, and wastes power. Noise from sensors often demands correction by the addition of filters in the control loop, again contributing phase lag and ultimately reducing stability margins.

Observers to the rescue
Observers are commonly used to determine internal states of a system based on measurements of other states. They're often used where states can't be measured because the sensor is either impractical or too expensive.

What is an observer? Basically, it is a mathematical structure that combines sensor output and plant excitation signals with models of the plant and sensor. For servomotors, plant-excitation signals refer to the torque-producing current, the current produced by the drive that powers the motor. The plant, in this case, is the servomotor and the sensor is the resolver. The power converter in servomotors is the current controller, or current loop. Observers work by combining knowledge of the motor, the power-converter output, and the feedback device to provide a feedback signal that is superior to that from a feedback device alone.

In some cases, observers can be used to make systems perform better. They can be more accurate than a physical sensor or can reduce the phase lag inherent in monitoring sensor output. Observers can also provide observed disturbance signals, which can be used to improve disturbance response. These signals approximate an external disturbance and are low-cost alternatives to directly measuring disturbance with a torque transducer, which can be many times the cost of the motor. However, observers are not a panacea. They add complexity to a system and require computational resources. They also may be less robust than physical sensors, especially when plant parameters change substantially during operation.

The observer reduces, or in some cases even eliminates, the phase lag caused by the RDC. The Luenberger observer combines two sources of information: the resolver output and the motor current. The observer uses the model to anticipate what the sensor signal will do and uses the sensor to correct itself. Often, the sensor is much slower than the calculation time involved. A typical sensor delay can be hundreds of microseconds, whereas the observer calculation time might be 2 or 3 msec.

Observers aren't as effective in applications with big changes in load inertia. In such cases, a physical acceleration signal as from a sensor may lessen this effect.

Aside from reducing phase lag in the control loop, another advantage is the derivation of observed acceleration. Observed acceleration can support acceleration feedback, which can be used to reduce problems with mechanical resonance. Acceleration feedback creates electronic inertia which increases the inertia of the motor, helping quell resonance. A physical acceleration sensor, such as an accelerometer, can also provide acceleration feedback, but such sensors are expensive.

Another benefit is the derivation of observed disturbance torque, which can be used to improve the disturbance response of the drive. This can also be used for disturbance decoupling, a technique where the disturbance signal is fed back with a polarity inversion to the power converter input. The use of disturbance decoupling greatly improves the dynamic stiffness of the system.