1 June 2002
Online Exclusive: Running without Sensors
By Koji Naniwa and Masayoshi Sato
Here's a new control method for three-phase induction motors.
The problem: A small induction motor needs some form of simple control. Our proposed speed control method uses a simple calculation, eliminating the need for a speed sensor. In this procedure, we estimate the load torque from the induction motor's detected power factor, while a frequency boost technique compensates the motor's speed. (The boost frequency is selected from a data table measured beforehand.) We obtained satisfactory experimental results with 90-W induction motors.
Motors are currently employed in numerous fields, and customer requirements are shifting from constant-speed to variable-speed designs. Moreover, in recent years there's been a growing demand for high-efficiency (energy-saving) models. The inverter drive method is being employed extensively to meet these requirements, while efforts are being made to research, develop, and commercialize high-performance controls, ranging from V/f to vector, in drive systems. However, there's also a demand for more simplified speed control in small AC motors and the like, where low cost is a requirement, but high response and a high-speed control cycle aren't needed.
Figure 1 shows the control method for AC motors, with particular emphasis placed on their characteristics. In recent years, the inverter-based V/f control has often been used as an AC motor speed control, making high-efficiency control possible over a broad speed range. However, there's the problem of a great speed variation due to slippage in the open control (without a speed sensor). Avoiding this problem (and ensuring precise control) requires a speed sensor. On the other hand, vector control, another favored approach, provides quick motor response and ensures high-precision control. Furthermore, a speed-sensorless vector control method has recently been developed. However, its complicated control implies a significant cost because it requires an instantaneous-current detector sensor or something similar.
As stated, the conventional inverter-based, speed-sensorless control is problematic in terms of both costs and characteristics. In an effort to solve these problems, we've developed a new (patent pending) control system for applications requiring a certain level of speed stability, where particularly high response and high-precision control aren't needed (Figure 2). This new system provides a speed sensor, hastens stability, and ensures low costs due to simplified control. What follows is an introduction to this new system's principles, the circuits adopted in the product, and the control method.
New System Characteristics
Figure 3 compares the rotary speed and torque characteristics of our new system (a) and a standard V/f control (b), using a 180-W induction motor. The principle difference is our system's improved speed stability. Its characteristics indicate that rotary speed is almost constant, despite the increased load torque, thus ensuring excellent speed control.
The BHF series, a speed control motor based on this system, is already in use commercially. It's highly valued for its outstanding speed stability and consequently employed in various types of automated equipment.
New Control System and Principle
Small AC Motor Characteristics
Subjecting an AC motor to control without a speed sensor makes it possible to estimate load torque from the primary current's magnitude. In the case of a small AC motor, however, there's little current variation with respect to load variation, due to the small primary current. When a current sensor is used for detection, it's more affected by noise, which makes using this method difficult.
On the other hand, it's relatively easy for us to detect the phase difference (Ø) between voltage and primary current. Again, with a small AC motor, the variation in Ø due to load variation is relatively great. Our newly developed control system detects the phase differences of voltage and primary current using a table of data characteristics, prepared in advance, to calculate the drive frequency corresponding to the load, thereby controlling the inverter frequency.
Equivalent Circuit
Figure 4 shows the AC motor's equivalent circuit (Type L).
We can describe the configuration along the current flow in this circuit as follows: It comprises an excitation circuit (parallel circuits g0 and b0), a stator circuit (circuits R1 and x1), a rotor circuit (series circuit x2´ and R2´), and mechanical outputs.
Let's discuss the motor's speed:
The motor's rotor speed N (rpm) can be expressed by the following equation:
(1)
where
| N0 synchronous speed s slip |
Likewise, synchronous rotary speed N0 is expressed as:
(2)
where
| f Power supply frequency (Hz) P Motor poles |
Now let's examine the equivalent current shown in Figure 4. We can express the power factor by the ratio between the equivalent circuit's resistance and total impedance. Ignoring the excitation circuit for the sake of a practical calculation, we can express the resistance with the following equation:
(3a)
(3b)
(3c)
Furthermore, the following equation gives us reactance:
(3d)
Thus, we express the power factor as:
(4)
From equation (4), it's clear that slide can be estimated via the phase difference if we know the motor's equivalent circuit because Ø denotes the phase difference between voltage and current. If we know the slide, we can estimate N from equation (1).
Furthermore, the AC motor output is expressed by the power consumed by the resistance R2´(1-s)/s. This is demonstrated by the following equation. (We're multiplying the right side by 3 because the equivalent circuit is designed for one phase.)
(5)
Phase voltage V1 is the inverter's set value. If we know the constant of the motor's equivalent circuit, we can obtain input current by circuit impedance (Ohm's law) and express it thusly:
(6)
We can estimate the power consumed by resistance R2´(1-s)/s-e.g., AC motor output, from equations (4) and (5):
(7)
Assuming rotary speed 
(rad/sec) and torque T (N·m) for the motor output, electric power given by equation (5) is converted into mechanical power:
(8)
The following relationship holds between (rad/sec) and N (rpm):
(9)
From these, we obtain the following:
(10)
Here, from equation (1), N = N0 (1-s). Thus, T can be given by:
If the equivalent circuit constant, s, N0, and V1 can all be known from equation (11), we can estimate T. From equations (1), (4), and (11), we know the constant of the motor's equivalent circuit, the number of motor poles P, applied voltage (phase voltage: V1), and power frequency f.
Thus, you see that we can estimate both N0 and T if we measure Ø.
Phase-difference Time
Figure 5 shows the phase-difference detection method. Two sinusoidal waves indicate the basic waves of primary current and voltage. This method detects Ø by measuring the time from the respective zero cross points of the voltage and current waveforms.
Voltage waveforms are signals issued by the inverter per se, so the zero cross point is clear. We can easily detect the time equivalent to Ø by measuring the zero cross point of the current waveform from the current converter's output waveform. Hereinafter, we'll refer to the time-converted value of Ø as "phase-difference time" (Øt).
Relationship between Øt and Inverter Frequency
Figure 6 shows the relationship between the inverter's output frequency and Øt when the test equipment (180-W induction motor) runs at a constant speed. The inverter controls frequency, ensuring that the rotary speed doesn't change even if the AC motor's applied Tload changes; we measure Øt at that moment and see that it decreases with the increase in torque. From this relationship, it's possible to estimate Tload at a given rotary speed from Ø.
Having estimated T, we can also estimate s. Therefore, we control the AC motor's speed by adjusting the inverter's output frequency, thus compensating for the slide's variation. For speed control, the characteristics shown in Figure 6 are stored as tabular data. We can calculate the inverter's output frequency by referring to this table when controlling the AC motor's speed. We make these computations using a linear interpolation approximation method (Figure 7).
Using this existing tabular data, we can compute both a table of rotary speeds and the inverter output frequency for the detected Øt. Given a rotary speed of 700 rpm, for example, we'd calculate the inverter's output frequency for Øt from data tabulated for 600 and 900 rpm (Table 1).
When the detected Øt is 4.3 msec, we base our computation on the inverter's output frequency data at phase differences of 4 and 5 msec in the table of computed data. This gives us an inverter output frequency of 27.6 Hz (Table 2).
We can conclude, tabular data notwithstanding, that speed control is possible at a given motor speed.
Practical Commercial Applications
In this system configuration (Figure 8), a pulse-width modulation (PWM) control-type inverter drives the induction motor IM. The drive voltage V applied to the induction motor and the current I detected by the current sensor CS are both input to the phase detector. Here, a timer within the microprocessor measures Øt from the zero cross point of the motor's applied voltage to the zero point of the current flowing to the motor and stores it in memory.
The inverter's output frequency characteristics with respect to Ø have already been measured (Figure 6), in order to maintain a constant speed when the load is changed. The ensuing measurement is also stored in the microprocessor's memory as a table of characteristics. Linear interpolation (Figure 7) via both this characteristic table and the detected Øt gives us the command value Nset for the speed setter's rotary speed preset. The resulting output is inverter output frequency f. In response, the V/f current computes the motor's corresponding applied voltage, which the PWM inverter uses to drive the induction motor, thereby performing speed control.
Consequently, we get a boost in the inverter's output frequency to compensate for any speed reduction arising from an applied load and thus achieve constant control of the induction motor.
Furthermore, such frequency increases compensate for not only speed variations but also speed constancy—even should variations occur in the motor or inverter temperatures or in the inverter's voltage supply, as well as in load torque.
Per this control method, Øt is the time between the zero crosses of current and voltage. Thus, as Figure 5 shows, Øt is detected twice for each cycle of inverter output frequency, and the detection interval is determined by that frequency. For example, the interval is 10 msec at 50 Hz and 50 msec at 10 Hz. Because we're detecting the average variation per cycle, we can't detect the instantaneous load variation. Thus, we can expect decreased control response, given the lower rotary speed. However, because the small AC motor's follow-up properties provide sufficient control time, we're ensured of sufficient applicability.
Characteristics
Figure 3a shows the rotary speed and torque characteristics of a product (BH series) based on this method. As illustrated, rotary speed is kept nearly constant despite variations in Tload. This denotes excellent speed stability. The following discussion of speed variation characteristics is with respect to load, voltage, and temperature and represents speed stability as a product specification, in addition to rotary speed and torque characteristics.
Speed Variation with Respect to Load
Speed variation with respect to load represents the difference in speeds when we apply a load of the rated torque, with respect to the rotary speed preset when there's no load. Table 3 shows the variation in speed with respect to load within the speed control range.
This indicates that the rotary speed is kept nearly constant in the speed control range, despite changes in Tload. This shows that both excellent speed stability and superior constant-speed control are ensured.
Speed Variation with Respect to Voltage, Temperature, and Speed
Tables 4 and 5 show, respectively, the speed variation in the event of deviations in supplied voltage to the product (rated voltage reference with respect to voltage) and the product's ambient operating temperature (reference of 25ºC with respect to temperature).
As with speed variation with respect to load, the rotary speed is kept nearly constant within the range of product specification, meaning there's excellent speed stability.
Our newly developed method obtains constant speed control, characterized by low cost and excellent speed stability, and gives particular attention to the phase difference Ø of primary current and voltage. The product using this system provides excellent speed variation characteristics within ±3%.
We can summarize our method's characteristics thusly:
Furthermore, we can encapsulate speed variation in the product (BHF series) based on this method as:
| Speed variation with respect to | Within ±3% of |
| Load | 0 to rated torque @1,500 rpm | Voltage | Power voltage ±10% @ 1,500 rpm, no load |
| Temperature | 0°–50°C @1,500 rpm, no load |
MC
Make Contact!
Koji Naniwa is a chief engineer at Oriental Motor Co. Ltd.'s Circuit Engineering Department for the ACIX division, located in Tsuruoka, Japan. Masayoshi Sato is chief engineer at Oriental Motor Co. Ltd.'s Product Research & Planning Department, located in Kashiwa, Japan. For further information, please contact Nick Johantgen, engineering manager, Oriental Motor USA Corp., 2580 West 237th Street, Torrance, CA 90505; tel: (310) 325-0040; fax: (310) 325-5280; www.orientalmotor.com.
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