an accurate auto-tuning procedure for encoderless ac · pdf filean accurate auto-tuning...

Transactions on Electrical Engineering, Vol. 3 (2014), No. 1 1

An Accurate Auto-Tuning Procedure for Encoderless AC Motor Drives in Industrial

Environments

Andreas R. Weber 1), Joachim Weissbacher 2), Gerald Steiner 1), Martin Horn 3)

1) Institute of Electrical Measurement and Measurement Signal Processing, Graz University of Technology, Austria,

e-mail: [email protected], [email protected] 2) Bernecker + Rainer Industrie Elektronik Ges.m.b.H, Eggelsberg, Austria, e-mail: joachim.weissbacher@br-

automation.com 3) Institute of Smart System-Technologies, Control & Mechatronic Systems Group, Klagenfurt University, Austria,

e-mail: [email protected]

Abstract — Modern ac motor drives are based on field oriented vector control with feedback and feedforward control units. The feedback control unit for position and speed consists of two cascaded standard PI-controllers. These controllers require information of the position and the derivative of the position, respectively. Typically a shaft encoder provides this information but more often a position observer is used instead. The feedforward control unit uses the set position trajectory in combination with mechanical parameters and essentially imposes the overall dynamics. This work presents a new method for self-commissioning of speed controller, position controller and feedforward control unit for drives without a shaft encoder. Performance and feasibility of the proposed method are demonstrated by experimental results.

Keywords — self-commissioning, feedforward control, encoderless, sensorless, flux observer, field oriented vector control, ac motor drives, frequency response measurement, maximum peak criteria

I. INTRODUCTION

Modern drive technology is often based on field oriented control structures. A typical controller structure of a field oriented vector controlled drive is shown in Fig. 1. The controller structure is composed of three cascaded controller loops. The innermost is the current controller loop which is composed of a standard PI-controller with electromagnetic force (emf) feedforward compensation. The controller parameters are adjusted automatically by the knowledge of the electrical motor parameters like resistances and inductances. Set value for the current controller (q-direction) is calculated by the superimposed speed controller whose actual value is given by the time derivative of the position signal. In order to suppress noise due to the quantization of the position signal a low pass filter is used in speed feedback loop. The corresponding set value of the speed controller is given by the position controller. Both, position and speed

controller are standard PI-controllers which are only used as proportional elements. The information of the known set position trajectory can be used to increase the performance of the command response. Based on identified mechanical parameters additive reference values for speed and quadrature current are calculated in the feedforward controller unit. The described field oriented control structure assumes exact information about the flux position. Typically a shaft encoder is used to provide the servo drive with this necessary position information. For lower investment costs, lower maintenance costs and increased reliability, the shaft encoder, the necessary cables and evaluation unit are saved and replaced by an observer. The usage of such an observer has an impact on the plant and therefore on the dynamics of the whole system. Since the commissioning of the current controller and the observer is assumed to be already completed, the parameters of the speed controller, position controller and feedforward controller unit have to be determined. Goal of this work is to present a method for self-com-missioning of these controllers and the feedforward controller unit which is characterized by simplicity for the user in terms of tuning parameters. In contrast to [1] where the mechanical parameters of two mass systems are identified (parametric model) in order to design a controller, in this work a nonparametric model is the basis for the design of the controllers. The parameters of the feedforward controller unit are identified by way of a point to point movement and an offline calculation. The work is organized as follows: In Section II the basics of the used observer is explained and compared. In Section III the identification and determination of feedback and feedforward controller parameters is shown. In Section IV experimental results are presented and Section V concludes the article.


II. ENCODERLESS CONTROL

A. Postion observer based on a flux estimator for a permanent magnet synchronous motor (PMSM)

The used position observer is a common flux observer in the stator fixed coordinate system ( ). Different methods of flux observation have been published, and some examples are reported in [2], [3], [4], [5]. Generally, the observer is estimated by the fundamental voltage equations.

(1)

(2)

Transformed into the flux vector

(3)

(4)

where is the stator resistance, the stator inductance, the measured current vector and the voltage vector.

With the stator fixed components and the position of the flux vector and commutation angle can be calculated via the arcus tangens function.

(5)

The problem with the open integration of the observer structure is avoided with a low pass filter and a feedback of the estimated flux error vector multiplied with a gain factor K. The error vector is the difference between the observed flux vector and a calculated reference flux vector. So unwanted influences based on current measurement errors, inadequateness in the voltage generation (e.g. nonlinear inverter voltage drop) and uncertain motor parameters are strongly reduced. The basic structure of the observer is shown in Fig. 2 as signal flow chart. The performance of the described position observer is shown in [6] and [7].

Figure 2: Signal flow chart of the flux vector estimator

Figure 1: Typical field oriented controller structure with feedforward controller unit


III. AUTOTUNING

AC Motors with position or speed observers, which are based on the fundamental equations, are not applicable at standstill or very low speed. Due to this fact operation at certain speed is necessary for identification of the overall system consisting of mechanics and observer [1], [8]. Since drive controllers are not parameterized yet, a provisory controller parameterization is necessary.

A. Provisory controller parameterization

In [9] a self-tuning speed control concept for drives with encoder is presented where a provisory PI speed controller with low bandwidth is used for performing experiments for estimation of the frequency response function (FRF). In contrast to [9] a proportional speed and position controller parameterized for a nominal value that equals to the motor inertia (known in the majority of cases out of datasheets) is used instead of the published PI speed controller based on the total inertia. The advantage of the missing integral part in the speed controller is that in case of a strong deviation of the actual inertia from its nominal value no unstable speed loop behavior can occur. Additionally to the given cascaded controller structure of the used servo drive there is a low pass (speed filter) in the speed feedback loop in order to smooth the quantization effects caused through the speed calculation

(6)

with a filter time constant and as sample time. The overall identification structure can be seen in Fig. 3.

Figure 3: Identification structure

By use of the "Magnitude Optimum" [10] both speed and position controller gains can be calculated as

(7)

(8)

with as the motor torque constant, the known motor inertia and the filter time constant of the

lowpass as a free design parameter. It should be mentioned that should be chosen in this case much greater than the sum of the small time constants (current controller loop) and dead times of the servo drive. Experiments on different mechanical setups showed that

is a reasonable start value for sufficient suppression of any existing resonances and high frequency noise.

B. Identification procedure

With the controller parameters of the previous chapter and a smooth position trajectory with a sufficiently small acceleration the drive can be operated at desired constant speed. The closed loop system is excited with a pseudo random binary signal (PRBS) as a disturbance signal in the torque generating component of the stator current [1], [8]. A PRBS of order can be generated by

(9)

with appropriate coefficients , , where is also the number of used shift registers. Useful coefficients for different orders can be found in [11]. The PRBS is periodic with discrete time steps. With a cycle time the necessary measurement time for one period is given by

(10)

As depicted in Fig. 3, the current (Input) and the differentiated position signal (Output) of the observer are used for calculation of the frequency response function. Therefore a discrete fourier transformation (DFT) of both input and output sequence sampled at

with sample time is performed. Element-wise division of the complex coefficients leads to the desired frequency response function

(11)

at frequencies . If exactly one period ( samples) is used after transient behavior has decayed no windowing technique and advanced signal processing is necessary to attenuate the leakage-effect. By use of an efficient fast fourier transformation (FFT) algorithm for calculation of DFT the estimation of the FRF can also be implemented on an embedded system with limited memory and calculation power. In Fig. 4 a FRF for a typical one mass system is depicted. As a reference the calculated FRF of the system with the installed encoder is shown. It can clearly be seen that at low frequencies both characteristics are very similar but at higher frequencies ( ) a differentiating behavior of the observer is obvious. The problem with increasing noise at higher frequencies can be avoided with the low pass filter (6) in feedback of the speed loop.


Figure 4: Comparison of measured FRF (one mass system) with

observer and encoder and a one mass model approximation for low frequencies

C. Speed controller tuning

Equation (11) can be interpreted as a nonparametric model of the plant for which the speed controller is designed in the following. Usually a parametric model is derived from the measurement data and used for further calculations. This parameter identification is a challenging task in view of an automatic procedure. Therefore a nonparametric model for numerically calculating the controller parameters is chosen. The open loop FRF of the speed controller is a series connection of the speed filter (6) evaluated at , the plant (11) and the controller gain .

(12)

The Maximum Peak Criteria [12]

(13)

is one possible way to formulate the design specifications in frequency domain in terms of gain margin (GM) and phase margin (PM) for the closed loop FRF

(14)

For a given upper bound a minimum gain and phase margin of the open loop system is guaranteed. In this work a value of resulting in and is chosen.

Figure 5: Proposed tuning algorithm for position and speed controller

The goal of the proposed tuning algorithm is to find a maximum value of the gain factor subject to the speed filter time constant and condition (13). In Fig. 5 (upper part) the main steps of the algorithm are presented graphically.


D. Position controller tuning

The identification of the position controller parameter is based on the calculated FRF of the closed speed loop

and an integrator from actual speed to actual position. Similar to Sec. III-C a gain factor of the position controller can be calculated for the open position loop FRF

(15)

as depticted in Fig. 5 (lower part).

E. Feedforward controller tuning

Since the positioning profile is usually known in advance, this fact can be used to improve the tracking behavior of the drive by means of speed and torque feedforward (feedforward controller unit). Whereas the speed reference is calculated by simply differentiating the position the torque reference is based on a simple one mass system with static and dynamic friction and can be calculated as:

(17)

(16)

It should be mentioned that the calculated feedforward torque has to be transformed into an equivalent current by

(17)

with the motor torque constant (see Fig. 1). To identify the parameters and movements with acceleration, constant speed and deceleration phases (speed trapezoidal) are necessary. Since the position and speed controller are already parameterized only the characteristics of the trajectory (distance, speed, acceleration) have to be determined. Usually the maximum distance is given by the hardware limits of the mechanics and the maximum speed by the nominal speed of the motor. The acceleration can be calculated via an estimated inertia ( ) which is based on a one mass approximation of the measured FRF (see Fig. 4) for small :

(18)

The set speed, set acceleration and resulting current signal for this excitation profile are used for identifying the parameters by solving the optimization problem:

(19)

In contrast to [13] where the identification of the feedforward parameters is carried out online, here the optimization is done offline in the rest time task. This has the advantage of less computation effort in the cyclic task.

IV. APPLICATION RESULTS

The used motor is a three phase permanent magnet synchronous motor (PMSM) from B&R connected with an extra flywheel ( ). The motor is fed by a B&R ACOPOS 8V1090.00-2 servo drive. Motor and servo drive parameters are described in the Appendix. The identified FRF of the speed controller plant is shown in Fig. 6

Figure 6: Comparison of measured FRF of the two mass system with

observer and encoder

and represents a typical two mass system with a resonance frequency at , an anti-resonance frequency at and an approximated mass moment of inertia of . The parameters identified with the presented method for the speed an position controller are given in Tab. I.

Table I: Controller Parameters

In Fig. 7 the FRF of the plant with observer, open and closed speed loop is shown. Fig. 8 represents the FRF of the position controller plant (closed speed loop in series with an integrator) as well as the open and closed position loop FRF. In the upper part of Fig. 9, the speed profile for the feedforward parameter identification is shown. In the


Figure 7: Calculated FRF for speed controller tuning

Figure 8: Calculated FRF for position controller tuning

Figure 9: Speed profile (top) and measured vs. identified torque

(bottom)

lower part the necessary measured torque for the given profile and the identified torque are depicted. The

identified parameter set is listed in Tab. II. By means of a typical positioning profile the performance improvement with the identified parameters is demonstrated.

Table II: Feedforward Parameters

The profile includes an acceleration phase from standstill, a constant speed phase and a deceleration phase to standstill. Note that the used observer can not be used in standstill, so an open loop current vector control is used for the region from standstill to . In this area the position controller error is forced to zero. Fig. 10 shows the reference position, reference speed and position error of a point to point movement with and without feedforward control. The acceleration and deceleration are set to a value that the necessary torque is half of the nominal torque of the motor. The occurred position error is described in units per revolution (1000 Units per revolution). The improvement with feedforward control is more than sufficient for a motor and servo combination without shaft encoder and can be useful for a lot of industrial applications.

Figure 10: Position profile (top), speed profile (middle) and position error for a point to point movement with and without feedforward

control (bottom)


V. CONCLUSION

This paper presents an acccurate method for parameterizing the position controller, speed controller and feedforward control unit in a field oriented controller structure without the position information of a shaft encoder. The need for an accurate position information and the possibility to observe this information via a flux observer are discussed. The structure of this position observer is described. A method to identify the FRF of the plant in combination with the position observer is shown. With the described maximum peak criteria the controller gains are determined. Furthermore a procedure for identifying the feedforward controller parameters is shown. Finally the performance and the feasibility of the proposed solution are demonstrated by means of a typical movement profile in industrial drive technology.

VI. APPENDIX

MOTOR: PMSM, B&R 8LSA36.E0030D200-0, NUMBER

OF POLE-PAIRS = 2, RATED VOLTAGE = 400V, RATED

CURRENT = 1.9A, RATED SPEED = 3000MIN , RATED

TORQUE = 2.7NM

INVERTER: B&R ACOPOS 8V1090.00-2, RATED

VOLTAGE = 3X400-480V, RATED CURRENT = 8.8A, WWW.BR-AUTOMATION.COM

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[9] H. Wertz and F. Schutte, “Self-tuning speed control for servo drives with imperfect mechanical load,” in Industry Applications Conference, 2000. Conference Record of the 2000 IEEE, vol. 3, 2000, pp. 1497 –1504 vol.3.

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