Vector control methods for induction machines: an overview <s> III. THE NOMENCLATURE <s> This paper synthesizes and develops a universal field oriented (UFO) controller for induction machines. The UFO controller decouples flux and torque in an arbitrary flux reference frame. Due to its high degree of generality the UFO controller lends itself to be fully compatible with all existing field oriented controllers, indirect as well as direct field orientation. As a consequence, the digital implementation of the UFO scheme is identical for all induction motor drives enabling the usage of identical hardware and software. Examples of UFO control block diagrams for different field oriented controllers are presented. The execution time of the UFO algorithm is compared with the classical rotor flux field orientation method when using a high speed digital signal processor. Further, this paper indicates that the flexibility of changing the flux reference frame can extend the stability region of the drive especially at high speed during flux weakening. Detuning problems in field orientation are handled in an optimal manner for each field oriented controller by proper selection of the model of the induction machine and its reference frame. > <s> BIB001 </s> Vector control methods for induction machines: an overview <s> III. THE NOMENCLATURE <s> 1. Elementary Principles of Mechanics.- 1.1 Newtons Law.- 1.2 Moment of Inertia.- 1.3 Effect of Gearing.- 1.4 Power and Energy.- 1.5 Experimental Determination of Inertia.- 2. Dynamics of a Mechanical Drive.- 2.1 Equations Describing the Motion of a Drive with Lumped Inertia.- 2.2 Two Axes Drive in Polar Coordinates.- 2.3 Steady State Characteristics of Motors and Loads.- 2.4 Stable and Unstable Operating Points.- 3. Integration of the Simplified Equation of Motion.- 3.1 Solution of the Linearised Equation.- 3.1.1 Start of a Motor with Shunt-type Characteristic at No-load.- 3.1.2 Starting the Motor with a Load Torque Proportional to Speed.- 3.1.3 Loading Transient of the Motor Initially Running at No-load Speed.- 3.1.4 Starting of a DC Motor by Sequentially Short-circuiting Starting Resistors.- 3.2 Analytical Solution of Nonlinear Differential Equation.- 3.3 Numerical and Graphical Integration.- 4. Thermal Effects in Electrical Machines.- 4.1 Power Losses and Temperature Restrictions.- 4.2 Heating of a Homogeneous Body.- 4.3 Different Modes of Operation.- 4.3.1 Continuous Duty.- 4.3.2 Short Time Intermittent Duty.- 4.3.3 Periodic intermittent duty.- 5. Separately Excited DC Machine.- 5.1 Introduction.- 5.2 Mathematical Model of the DC Machine.- 5.3 Steady State Characteristics with Armature and Field Control.- 5.3.1 Armature Control.- 5.3.2 Field Control.- 5.3.3 Combined Armature and Field Control.- 5.4 Dynamic Behaviour of DC Motor with Constant Flux.- 6. DC Motor with Series Field Winding.- 6.1 Block Diagram of a Series-wound Motor.- 6.2 Steady State Characteristics.- 7. Control of a Separately Excited DC Machine.- 7.1 Introduction.- 7.2 Cascade Control of DC Motor in the Armature Control Region.- 7.3 Cascade Control of DC Motor in the Field-weakening Region.- 7.4 Supplying a DC Motor from a Rotating Generator.- 8. Static Converter as a Power Actuator for DC Drives.- 8.1 Electronic Switching Devices.- 8.2 Line-commutated Converter in Single-phase Bridge Connection.- 8.3 Line-commutated Converter in Three-phase Bridge Connection.- 8.4 Line-commutated Converters with Reduced Reactive Power.- 8.5 Control Loop Containing an Electronic Power Converter.- 9. Control of Converter-supplied DC Drives.- 9.1 DC Drive with Line-commutated Converter.- 9.2 DC Drives with Force-commutated Converters.- 10. Symmetrical Three-Phase AC Machines.- 10.1 Mathematical Model of a General AC Machine.- 10.2 Induction Motor with Sinusoidal Symmetrical Voltages in Steady State.- 10.2.1 Stator Current, Current Locus.- 10.2.2 Steady State Torque, Efficiency.- 10.2.3 Comparison with Practical Motor Designs.- 10.2.4 Starting of the Induction Motor.- 10.3 Induction Motor with Impressed Voltages of Arbitrary Wave- forms.- 10.4 Induction Motor with Unsymmetrical Line Voltages in Steady State.- 10.4.1 Symmetrical Components.- 10.4.2 Single-phase Induction Motor.- 10.4.3 Single-phase Electric Brake for AC Crane-Drives.- 10.4.4 Unsymmetrical Starting Circuit for Induction Motor.- 11. Power Supplies for Adjustable Speed AC Drives.- 11.1 Pulse width modulated (PWM) Voltage Source Transistor Converter (IGBT).- 11.2 Voltage Source PWM Thyristor Converter.- 11.3 Current Source Thyristor Converters.- 11.4 Converter Without DC Link (Cycloconverter).- 12. Control of Induction Motor Drives.- 12.1 Control of Induction Motor Based on Steady State Machine Model.- 12.2 Rotor Flux Orientated Control of Current-fed Induction Motor.- 12.2.1 Principle of Field Orientation.- 12.2.2 Acquisition of Flux Signals.- 12.2.3 Effects of Residual Lag of the Current Control Loops.- 12.2.4 Digital Signal Processing.- 12.2.5 Experimental Results.- 12.2.6 Effects of a Detuned Flux Model.- 12.3 Control of Voltage-fed Induction Motor.- 12.4 Field Orientated Control of Induction Motor with a Current Source Converter.- 12.5 Control of an Induction Motor Without a Mechanical Sensor.- 12.5.1 Machine Model in Stator Flux Coordinates.- 12.5.2 Example of an "Encoderless Control".- 12.5.3 Simulation and Experimental Results.- 12.6 Control of an Induction Motor Using a Combined Flux Model.- 13. Induction Motor Drive with Reduced Speed Range.- 13.1 Doubly-fed Induction Machine with Constant Stator Frequency and Field-orientated Rotor Current.- 13.2 Control of a Line-side Voltage Source Converter as a Reactive Power Compensator.- 13.3 Wound-Rotor Induction with Slip-Power Recovery.- 14. Variable Frequency Synchronous Motor Drives.- 14.1 Control of Synchronous Motors with PM Excitation.- 14.2 Synchronous Motor with Field- and Damper-Windings.- 14.3 Synchronous Motor with Load-commutated Inverter (LCI- Drive).- 15. Some Applications of Controlled Electrical Drives.- 15.1 Speed Controlled Drives.- 15.2 Lineax Position Control.- 15.3 Lineax Position Control with Moving Reference Point.- 15.4 Time-optimal Position Control with Fixed Reference Point.- 15.5 Time-optimal Position Control with Moving Reference Point. <s> BIB002
The first proposal of a vector control method has been presented by Blaschke  using the space vector notation suggested by Kovacs  , [12] . Since the 1980s new approaches for vector control methods have appeared in the literature: Yamamura (phase segregation, spiral vectors); Takahashi ( -components); Depenbrock ( components); De Donker (generalized -components). Other proposals are basically a direct consequence of these. For the present paper, the -notation used by De Doncker and Novotny BIB001 was chosen since it allows the machine representation in arbitrary reference frames (e.g., stator flux, rotor flux, air-gap flux, etc.) with relative simplicity. This notation is a generalization of the classical -notation  where the reference frame speed is no longer restricted to constant values. The relationship between space vector, spiral vector, and -notations is presented during classes. With the De Donker's notation BIB001 , it can be shown that the induction motor model, assuming impressed stator currents, is given by where dispersion factor; arbitrary turn ratio, which physical meaning is given below for three different values; pole pair number; flux slip frequency; component of the arbitrary flux based on the reference frame linked to the arbitrary flux vector; stator current component; stator current component; rotor inductance; air-gap inductance; stator inductance; rotor resistor; electromagnetic torque. The reader should pay attention to the character " " that is used as a subscript and superscript to identify the arbitrary reference frame and also as a letter that represents turns ratio. This choice may appear confusing, but it is a good way to point out that the arbitrary reference frame depends just on the choice of a turn ratio. These equations are presented as a block diagram in Fig. 1 where the coupling effect of the current components on the flux and torque can be observed. The "stator voltage/stator current" model of an induction machine allows different equivalent models with different internal variables. This is a point stressed in good books on electrical machines, e.g.,  , BIB002 ,  . Additionally, according to the value of , , which is an internal variable, assumes different meanings: then (stator-flux); then (air-gap flux); then (rotor-flux). This approach corresponds to the field orientation model proposed by Blaschke  . As can be seen from this block diagram, the flux can be controlled independently by ; whereas, the torque is controlled by changing , maintaining the rotor flux constant.