“The simplest control technique used today is Volts per Hertz. It is conceptually simple and easy to implement on a basic microcontroller. The core algorithm exploits the core characteristics of AC motor design. Each motor has a characteristic magnetizing current and maximum flux and torque produced. These properties are related to the volts-per-hertz ratio. The motor is rotated by switching of stator coils arranged around a moving rotor that rotates the mechanical load.
Author: European Editors
By 2035, the world will consume more than 35 trillion kWh of electricity annually, up from less than 21 trillion kWh in 2015. Today, nearly one-third of the electrical energy required by motors used in industrial production. Many of these motors are based on simple AC designs because they are relatively low cost and easy to drive. They are also very inefficient in terms of energy usage, especially at low speeds. However, such AC motors are not inherently wasteful. With the right form of Electronic control, their efficiency can be significantly increased. Using today’s available control technology, energy consumption for a given operating level can be reduced by up to 60%.
The simplest control technique used today is Volts per Hertz. It is conceptually simple and easy to implement on a basic microcontroller. The core algorithm exploits the core characteristics of AC motor design. Each motor has a characteristic magnetizing current and maximum flux and torque produced. These properties are related to the volts-per-hertz ratio. The motor is rotated by switching of stator coils arranged around a moving rotor that rotates the mechanical load. Switching between coils forces the magnetized elements of the rotor to rotate in synchrony to move to a steady state where the magnetic field remains in balance.
An increase in the coil switching frequency in turn increases the speed. However, if the supplied electrical energy does not increase accordingly, the applied torque will drop. Voltage-per-Hertz control provides a simple solution to the problem by increasing the line voltage as the frequency increases so that the torque can be kept at a constant level. Unfortunately, this relationship isn’t particularly consistent at low speeds. Higher voltage is required to maintain high torque at low speeds, but efficiency drops and increases the likelihood of coil saturation and overheating.
Field-oriented control provides a way to optimize motor control, especially at low speeds, and also provides the ability to make motor positioning control more precise. This increases the overall range of applications for AC motors, helping to reduce the cost of industrial machinery as well as operating costs.
In field-oriented or flux vector control, the link between speed and torque implied by volts-per-hertz control is broken. The concept of field-oriented control can be expressed using a wound DC motor model, where the currents supplied to the stator and rotor are independent. In this model, the generated torque and flux can be independently controlled. The strength of the magnetic field generated by the current in the motor unit determines the magnetic flux. The current supplied to the electromagnetic windings in the rotor controls the torque – as the magnetic field tries to tune itself to a steady state.
DC motors use a commutator on the rotor that does the job of controlling which coils on the stator are energized at any time. The commutator is designed so that the current is switched to the mechanically aligned windings to produce maximum torque at that point. Therefore, the windings are managed in such a way that the magnetic flux changes to keep the rotor windings orthogonal to the magnetic field produced in the stator.
In an AC motor, only the stator current is directly controlled. The rotor typically uses permanent magnets to provide its magnetic field. This means that the flux and torque depend on the same current. But field-oriented controls provide the ability to manipulate them almost independently. In practice, the stator flux is dynamically controlled to provide the ability to manipulate torque independently. Typically, stator coils can be driven so that they generate torque or apply force along the stator axis, a mode that does not affect rotation. These directions are the orthogonal axis and the straight axis, respectively. To transmit motion, each coil is driven in turn to generate a high normal force.
Several mathematical transformations are used to provide the capability of current and voltage changes to decouple torque and magnetic flux. Under field-oriented control, the current flowing through different parts of the stator is represented by a vector. Matrix projection transforms a three-phase time- and velocity-dependent system into a two-coordinate time-invariant system. The coordinates are usually described using the symbols d and q, which represent the flux and torque components, respectively. In the (d,q) reference frame, the applied torque is linear with the torque component.
Under field-oriented control, electrical signals are received from the motor and incorporated into the (d,q) coordinate model. The model is usually calculated relative to the rotor, making it easier to calculate the required flux. A typical method for computation is paired Clarke and Park transforms.
The Clarke transform takes currents from different phases (usually three phases) and uses them to estimate the currents in a Cartesian coordinate system. The axes of these systems use the symbols alpha and beta instead of the traditional x and y to reduce the possibility of confusion with spatial coordinate systems. These are then applied to the Park transformation to provide the current vector as seen in the rotated (d,q) coordinate system. Trigonometric functions provide the core of the conversion and require the use of a microcontroller or digital signal processor (DSP).
The flux and torque components of the current vector in (d,q) space are derived from the current and rotor flux positions fed into each electrical phase via Clarke and Park transformations, using the symbolic theta algorithm in most descriptions. This structure is suitable for a range of motors. The Inverse Park Transform is used to generate a voltage output, which is then used in an algorithm that controls the power in each of the three phases. The overall structure is shown in Figure 1.
Figure 1: Basic configuration of the transform and control block for field-oriented control.
The same core structure can be used to control both synchronous and induction machines by simply changing the flux reference and obtaining the rotor flux position. In a synchronous permanent magnet motor, the rotor flux is fixed because it is determined by the permanent magnets. Induction motors need to generate rotor flux to operate, so this is incorporated into the flux reference as a non-zero value.
The key to the success of field-oriented control is the real-time prediction of the rotor flux position. There is a complexity to this control strategy. Inside an AC induction motor, the speed of the rotor does not match the speed at which the magnetic flux driving it spins. The rotor tends to lag, causing a difference called slip speed. In the old scheme, motor manufacturers used sensors to analyze rotor position, but this resulted in unnecessary additional costs. In practice, feedback from the voltage and current generated within the motor can be used to compensate for slip.
Many systems use the measured back EMF to estimate rotor slip. The magnitude of the back EMF voltage is proportional to the speed of the rotor. However, using this input directly at low speed or stationary can cause problems, and the initial position is not easy to estimate. Starting from an unknown rotor position may cause the motor to reverse unexpectedly a short distance or fail to start completely. Another disadvantage of simply sampling the back EMF is its sensitivity to stator resistance, which tends to vary with temperature.
The indirect model-based scheme provides better performance. There is a large trade-off between computational overhead and performance, but in general efficiency can be improved by using more complex model-based algorithms, especially at low speeds. Model-based indirect approaches estimate real-time values of these based on available sensor readings.
As with back EMF estimation, the core problem is to determine the starting point of the motor. One solution is to start with an estimate of the initial state from which a vector of predicted outputs can be derived and compared to the measured output vector. This difference is used to correct the internal state vector of the model. However, noise can destabilize the model.
The extended Kalman filter can compensate for the effects of noise and burst interference. The architecture of the Kalman filter allows updates that are considered to have lower uncertainty to be given a higher weight than updates that are estimated to have greater uncertainty. The filter works recursively, so only a new set of readings and the previous state of the filter are required for each estimation to generate a new state.
The Kalman filter employs two main stages: prediction and update. In the prediction phase, the filter calculates the next state of the system based on the previous state, and in the case of motion algorithms, it provides the last known velocity and acceleration values. From this, the filter computes a prediction for the current location.
During the update phase, the newly sampled voltage and current values are compared with their predicted values. The closer the input data is to the prediction, the lower the probability of error. This error probability is fed back into the Kalman filter gain. At the algorithmic level, Kalman filters rely on many matrix multiplications and inversions. Therefore, the key to implementing extended Kalman filters in motor control is high arithmetic performance, as in other aspects of field-oriented control.
To implement the many arithmetic operations per second required in real-time motor control situations, a high-performance MCU or DSP is required. The TMS320F2833x family of devices from Texas Instruments are designed to handle the computing loads typical of AC motor applications and are supported by a variety of on-chip peripherals to aid integration with power conversion electronics.
The TMS320F2833x is built around a high-performance 32-bit CPU with floating point support, compliant with the IEEE754 single-precision arithmetic standard. By implementing an IEEE-compliant floating-point unit, the TMS320F2833x simplifies algorithm development because it can handle a very wide range of numbers and has built-in support for errors such as not-a-number (NaN) and divide-by-zero conditions. The Harvard architecture coupled with dual 16 x 16 multiply-add (MAC) units provides high throughput for matrix- and projection-based operations. For improved accuracy, these units can be linked together to perform a 32 x 32 MAC. The on-chip peripherals include a 16-channel analog-to-digital converter (ADC) for sampling the voltage and current feedback signals from the motor.
A member of the C2000 family of DSP-enhanced MCUs, the TMS320F2833x is supported by TI’s Digital Motor Control library, which provides reusable, configurable software blocks to implement various control strategies. The library consists of functions represented as blocks that provide transformations such as Clarke and Park, in addition to control blocks for closed-loop operation and peripheral drivers for functions such as pulse width modulation (PWM).
In the case of motor control, the PWM output controls six power transistors, which together provide voltage and current to the three electrical phases. Each phase uses a half-bridge transistor configuration. A common algorithm for control in these cases is space vector PWM. This reduces harmonics and uses eight switching states compared to simpler PWM techniques. There are six active states and two zero states, each of which is the target state of eight corresponding space vectors. The states are arranged in such a way that two sets of complementary states are active at all times. One set is for the three high-side power transistors and the other is for the low-side. The algorithm loops through the states to switch power sources to states as required by the field-oriented control model. The TMS320F2833x includes PWM hardware suitable for software control using space vector switching. Six out of a total of 18 PWM outputs support high-precision control with a resolution of 150 ps. The result is a digital controller that requires relatively little external hardware to manage the power transistors, as shown in Figure 2.
Figure 2: Block diagram showing the control of power supply phases by the F2833x’s PWM outputs.
Using a microcontroller with the necessary core and high-performance building blocks, combined with TI’s digital motor control library, designers can drive a new generation of high-efficiency AC motors.