Sensorless Estimation for Hybrid Stepper Motors

Good motor positioning repeatability and the capability to detect lost steps is of great importance for a proper operation of the collimators. It is thus necessary to have real-time knowledge of the motor position in order that compensatory action can be taken to correct any misalignments.

However, working in a high radiation environment makes things more difficult than usual. Most position and torque sensors do not function correctly in these working conditions, and even though there are sensors like the Linear Variable Differential Transformer (LVDT) or the resolver that can be constructed to be radiation-hard, the system cannot rely solely on them since failure is not affordable: intervention in the collimation areas is extremely difficult and expensive due to the radiation, even during the machine technical stops.

In addition, even if the stepping motors work at nominal torque, chosen by design to be at least twice the nominal load torque, having an estimate of the real load torque can be useful to warn of mechanical degradation. All the LHC collimators have passed acceptance tests where the load torques over the entire axes strokes have been measured and verified. Load torque warning thresholds can be easily determined for each collimator axis according to the collimator type and orientation.

For the aforementioned reason, high robustness is mandatory. Failure of the sensors must not be critical, and therefore redundancy through sensorless methods is desirable.

With the increase in power and decrease in cost of embedded processors in recent years, the drives used to power and control stepper motors have become increasingly sophisticated. For example, in compensation of the detent torque and several harmonics of the HSM in the quadrature axis component of the current is proposed, both for use in open loop, where the angle used for the Park Transform is the command position, and closed loop, where an encoder is used for position information, in order to prevent the motor characteristic resonances. Improved diagnostics can thus be achieved through the use of sensorless algorithms instead of via additional sensors, with their associated higher costs and lower reliability.

Sensorless position and torque estimation techniques have been applied to Hybrid and Permanent Magnet Stepping Motors previously, largely due to the vast increase in computational power in modern embedded devices, such as Digital Signal Processors (DSP), at ever decreasing costs. Does a review of position estimation techniques for brushless permanent-magnet machines, by measurement of the back electro-motive force, the inductance variation and the flux-linkage variation, using direct estimation methods or observers. A similar review is focusing on brushless DC motors, but in addition the current injection method is considered and the estimation is presented for generators as well. Presents a review of high frequency injection methods for rotor position estimation.

A number of torque and position estimation techniques for stepping motors have been proposed using different methods. In a disturbance observer is proposed for use with permanent-magnet stepper motors. Focused on hybrid stepper motors are some examples like, where a torque estimation technique without the feedback of speed or position sensors is proposed, and, where a damping control system using a speed and position observed based on a phase locked loop that tracks the phase angle of the back electro-motive force voltage is presented. However, unlike the Extended Kalman Filter, they do not provide a unified method for full state estimation, rather only concentrating on a single signal.

Despite its relatively high computational complexity, the Kalman Filter, and more specifically the Extended Kalman Filter (EKF), has become one of the favored approaches for sensorless position estimation in electric motors. For example in the EKF is used to estimate position and angular speed in a permanent magnet synchronous motor drive and these estimations are used to close the angular control loop. In the EKF is applied to estimate the same states for a brushless DC motor, with the addition that the filter is implemented both with fixed motor parameters and with online estimation of the stator resistance, allowing for an improvement of the estimation especially at low speeds.

The Kalman Filter estimates the motor states in a statistically optimal way despite the presence of both measurement and process disturbances. Furthermore, unknown inputs to the motor, such as an external load torque, can also be estimated in a structured way. This method has been used in different aspects of industry.

In addition, the proposed philosophy to applying an EKF to a drive connected to a stepper motor by long cables is completely general and could be applied to other types of motors connected in this way, as are commonly found in particle accelerators, nuclear power plants, oil extraction or underwater applications. In the food industry motors are placed in clean areas far from the drives. Even in some cases aerial vehicles use a long cable connecting the motor.

The utilization of the EKF with HSM connected through long cables can be achieved successfully. Sensorless estimation allows the angular position of the motor to be estimated in real-time by optimally combining measurements of the motor electrical signals, current and voltage, with the prediction of a model of the motor. However, a consistent mismatch between the predicted voltage in the motor phase using the standard model for the HSM found in literature and the experimental results was noticed. In Fig. 1 this effect is shown: there is a discrepancy when the phase has a non-zero current.

Discrepancy between measured voltage and standard model prediction
Figure 1: Discrepancy between measured voltage and standard model prediction

HSM modelling has received attention in the literature and typically the models fall into two categories, either for motor design or for control. Despite attempts to develop simpler models and analysis techniques e.g., models for motor design are normally of such high complexity that their use in real-time algorithms running on embedded processors is not possible. Models for control are at the other end of the complexity spectrum, being generic models that apply not only to HSMs, but also to Permanent Magnet Stepping Motors (PMSMs) and even more generally to permanent magnet AC synchronous motors. Practically all the references given for the use of EKF on HSM fall into this category.

This observation leads to the goal of improving the motor model whilst keeping it usable for real-time applications in embedded systems. Two extensions to the standard model of the electrical subsystem of an HSM, dependent on the rotor position and phase current respectively. A combined model, which is simultaneously dependent on position and current is developed as well and magnetic theory is used to give an expression of the predicted electromagnetic torque. To demonstrate its success at reaching the goal, it is used in a real-time application.

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