The past few decades have seen a rise in the use of field-oriented control in induction motor applications. One advantage of field-oriented control - or as some call it, vector control - is that it increases efficiency, letting smaller motors replace larger ones without sacrificing torque and speed. Another advantage is that it offers higher, more dynamic performance in the case of speed and torque-controlled ac drives.

Field-oriented control drives also offer several benefits to the end user. They are smaller than the trapezoidal commutation drives they replace. They also offer more efficiency and higher performance at the same time, without demanding tradeoffs. In addition, servo drive manufacturers are leveraging processing power to add more features such as power factor correction, which eases the harmonics and power factor issues that system designers must address.

### Overcoming obstacles

In developing field-oriented control technology, engineers have faced and overcome several obstacles. For one, calculations associated with vector control are far more demanding than those associated with traditional (scalar) techniques. Where standard microcontrollers wouldn't work, digital signal processors (DSPs) provided the edge.

DSPs more than double induction motor operating efficiency from 40% (typical of microcontroller-based solutions) to as high as 90% by injecting energy into stator at more optimum times. This type of smarter control also improves power factor ratios - something that local utilities usually reward - and lets design engineers spec low-horsepower motors confidently, instead of over-sizing the motor to make up for inefficient operation.

Until recently, the drawback of using DSPs - and thus field-oriented control - was that DSPs were not as capable as microcontrollers in the realm of straightforward control operations. But this has changed with the addition of many peripherals now found in DSP architectures, along with architectural adjustments to accommodate the special needs of field-oriented control algorithms.

### Sensor issues

Another challenge for engineers developing field-oriented control applications had to do with measuring rotor data. Early-generation vector-controlled ac motors employed high-precision speed sensors, but added costs and reliability issues posed a significant drawback. Sensorless control appeared to be the answer, but it has been found to have serious limitations in practical applications. The main problem stems from sensitivity to parameter variations, such as stator resistance changes. This has a significant impact on efficiency at low speeds, and remains a barrier to widespread use of sensorless control.

As a result, engineers today are faced with a dilemma. They can use high-precision sensors, which provide accurate measurements, but present robustness issues in hostile environments. Or they can use tougher, low-cost sensors and try make up for accuracy limitations by employing more sophisticated processing methods.

DSPs and the promise of even faster processors in the future clearly favor the latter approach. In fact, by combining DSPs, low-resolution speed sensors, and enhanced parameter estimation techniques, engineers are achieving the full benefit of field-oriented control in systems costing little more than standard ac drives.

The heart of the solution is an algorithm that compensates for motor slip frequency error. This error is the result of variations in rotor time constant. Uncertainties associated with these variations tend to detune vector-control systems. Fortunately, the newly developed correction procedures don't need to know motor parameters because they're implied from other known data. As a result, uncertainties and detuning are no longer at issue.

### Field control basics

Three-phase motors usually incorporate windings that are separated by one-third phase (or a fraction of that) along the stator. Feeding the windings with three voltages separated in phase by one-third of a cycle produces a rotating magnetic field.

The rotor in an induction machine is a closed circuit. In the case of a squirrel cage rotor, the circuit consists of conductor bars shorted together with thick end rings. When the stator magnetic field sweeps the rotor, it creates an induced magnetic field that interacts with the stator magnetic field, producing motor output torque. The magnitude of the torque is proportional to the cross product of the rotor and stator flux. This means that for a given machine configuration, the torque production is determined by the strengths of the two magnetic vectors, and the sine of the angle between them.

For design engineers, the key takeaway of this analysis is that a vector control scheme for an induction machine must be capable of estimating the correct angular position of the rotor magnetic flux in order to achieve effective torque generation.

### Effect of parameter variation

In a conventional feed-forward field orientation system, the two current components controlling flux *i ^{*}_{ds}* and torque

*i*are considered the input commands. The reference-input value of the rotor time constant

^{*}_{qs}*T*is used with the input current to calculate the input command slip frequency

^{*}_{r}*u*.

^{*}_{slip}Detuning caused by parameter variation and its effects on flux and torque is shown mathematically in *Equation 1*. The steady state induction motor output torque is:

Under field oriented conditions, with the correct gain in the slip calculator, slip can be calculated as follows:

Substituting *Equation 2* into *Equation 1* yields the desired linear relation between torque and its command. If, however, there is a mismatch between motor and model parameters, the slip frequency gain is not calculated correctly. This mismatch can be represented by a scalar a called slip frequency gain. In this case we have:

It is easy to see now that the desired cancellation of the nonlinear terms in *Equation 1* will not occur unless motor and model parameters match. And this, in turn, is what causes detuned operation and less than optimal dynamic performance.

### Self-tuning procedure

Operation at maximum torque per ampere is obtained when, at a given torque and speed, the stator's current amplitude is minimized. The slip frequency at which the torque per stator ampere is maximized can be extracted from conventional equations but again, this frequency is subject to error due to parameter variation.

This calls for a special control system, similar to a conventional one, but with an additional tuning block that adjusts slip frequency gain. The tuning block's key function is to identify the rotor time constant properly.

A useful set of characteristic torque curves can be obtained by substituting *Equation 3* into *Equation 1*. By normalizing the results we get:

Where:

The normalized torque *T _{N}* can be interpreted as the torque per unit based on the field-oriented torque that exists when

*i*= 1.0. Torque characteristics are best viewed by plotting normalized torque

_{qs}/i_{ds}*T*as a function of the gain error α. The vertical line at α = 1.0 represents the field-oriented operation. Note that along this line, the torque is a linear function of

_{N}*i*.

_{qs}/I_{ds}The plot shows that vector control does not provide maximum torque per stator ampere unless *i _{ds}* is equal to

*i*. Operation at maximum torque per ampere is obtained whenever the stator current amplitude is minimized for a given torque and speed.

_{qs}Referring back to the proposed control system, the tuning block is responsible for adjusting the slip frequency gain in the vector control block diagram. The key here is to identify the rotor time constant with sufficient accuracy.

### How it works

When the tuning procedure begins, the speed controller is bypassed and its function preformed by the tuning block. Based on the amplitude of *i _{ds}* and

*i*, motor current amplitude will change in order to maintain constant motor speed, with

_{qs}*d*and

*q*current amplitudes being equal. In this step, produced torque is controlled by the change in slip frequency gain.

In the next step, slip frequency is changed linearly, such that *i _{ds}* and

*i*vary but do not exceed their maximum allowed value. During this change, the minimum value of the

_{qs}*i*(=

_{qs}*i*) and corresponding slip gain are recorded.

_{ds}During these two steps, speed is regulated and remains constant. The slip frequency gain obtained at the second step is the tuned one. By obtaining the tuned slip frequency gain, the tuning block is removed from the control system and the speed controller is placed back in the control loop. Before closing the loop, the output of speed controller must be adjusted to match the current and avoid any sudden jump in the control system.

Besides tuning the slip frequency gain, this procedure can be used to achieve maximum torque per stator ampere whenever the motor is running in a steady state condition. In order to avoid saturation, however, which results in problems such as overheating, *i _{ds}* should not exceed its rated value.

Developed torque must remain constant during this procedure. To keep it constant under steady state load, the algorithm regulates the speed at its reference value in the low-speed region and calculates the developed torque in the high-speed region. However, during the transition - or in case of load change at low speed - the torque will change in order to regulate speed, and the tuning procedure will not be valid.

To detect transients in the load in the low-speed region and avoid running the self-tune procedure, a halt signal is sent to the tuning block if it detects a change of more than 5% in calculated developed torque. In this case, the tuning block stops tuning until the next tuning period. The developed torque can be calculated as:

where

*For more information, contact Kedar Godbole, Motion Control Strategist, Texas Instruments, via e-mail at* controlanswers@list.ti.com.

### Getting more from field-oriented control

Determining rotor position under all circumstances and at a reasonable cost is an on-going engineering challenge, particularly since the operating environment of induction motors can be both harsh and variable over time. What's most affected by environment are rotor and stator time constants. These typically vary with time and are particularly sensitive to temperature-induced changes in rotor resistance.

Over the full operating temperature range of a typical induction machine, rotor resistance can easily vary by about 50%, corresponding to a 33% change in the rotor time constant. Without employing some form of self-tuning technique, the torque degradation in the “bare bones” field-oriented control can be on the order of 29% or more. From a design perspective, this means that in many applications where vector control is used to save energy, the motor must still be oversized. Despite the advantages of field-oriented control, much remains to be gained in terms of motor size and cost.

By adding self-tuning algorithms, it is possible to limit torque degradation to between 3% and 7%. For most applications, this is an acceptable range, meaning that a typical induction machine application can be designed with a smaller, cheaper motor, thus resulting in cost savings at the same time as improving the performance.

### Dialed in for motors

Implementing advanced field-oriented control algorithms demands significant computational bandwidth. Because of this requirement field-oriented control has been overly complex, costly, and restricted to a narrow range of applications. The advent of modern digital signal processors, however, has made field-oriented control the relatively straightforward solution that it is today.

DSP-based controllers incorporate very powerful number crunching cores: up to 32-bit, 150 MIPS for motor control customized DSPs. With such power, DSPs can implement control laws and reference-frame translations at high sample rates, resulting in very high current loop bandwidths. This, in turn, ensures fast servo response times and precise transient control.

The key distinguishing feature of DSP-based controllers is their bus architecture, which allows the efficient movement of data to and from the DSP's single-cycle multiply-and-accumulate processing cores. Lightning fast, DSPs can perform rotor positioning and speed calculations in real time without lookup tables. Some DSPs even incorporate motor control peripherals such as PWM outputs, a/d converters, flash memory, and on-chip CAN bus.

Keeping pace with hardware, and just as important, are software advances. Today's extremely efficient C compilers let developers create object code nearly as compact as native assembly language. The compilers yield excellent performance and C-to-ASM ratios of 1.1, which means that designers are free to think creatively about their systems and how to improve them.