The complex spatial stator current vector is defined in the coordinate system (d, q) where orthogonal components belong to the straight (d) and quadrature (q) axes. In that way, the magnetic coupling component of the current field is assigned to the d axis while the current torque component is assigned to the q axis [20]. Moreover, the described system of coordinates (d, q) for the induction motors is superimposed on the three-phase sinusoidal system of the instantaneous motor (a, b, c). The components (d, q) of the system's current vector permit standard control regimes including integral, proportional, or PI control, similarly to a DC motor case [21]. The (d, q) coordinate system projections generally include:  
* The direct projection of instantaneous currents to a complex spatial vector representation (a, b, c) of stator currents, using a three-phase sinusoidal system;
* The direct two-phase projection of (a, b, c) onto (\(\alpha\),) utilising the Clark transform. For the implementation of vector control, a motor with balanced three-phase currents is standardly assumed providing those two phases of the motor current are to be measured only. In addition, the reverse projection from (\(\alpha\),) to (a, b, c) utilises an inverse Clark transform or PWM modulator space-vector along with one of the diverse PWM modulators [22]. The Clark transform is utilized in order to convert a system of three-phase currents and voltages into a two-coordinate time-independent linear system. This makes it possible to utilise uncomplicated and easy-to-implement PI controllers, as well as to simplify the control of currents that generate magnetic flux and torque [23]. The rotation speed of the (d, q) coordinate system may be adjusted to any intended value. However, there could be preferred following speeds of the reference system:  
* Non-rotating (d, q) coordinate system within the stationary reference frame;
* The (d, q) coordinate system rotating at a synchronous speed within the reference system;
* The coordinate system (d, q) rotates at a rotor speed within the rotor reference system. In order to find an effective control algorithm, the torque and excitation currents may be inferred using the original stator current inputs. In DC motors, the magnetic field and torque components may be relatively simply controlled using the separate controlling of the corresponding field and armature currents. The economic control of variable speed AC motors requires microprocessor control with AC drives using a high-performance digital signal processing (DSP) technology [24]. Inverters have good potential for the sensorless or feedback-including implementation. Their key limitation in the case of a non-feedback operation is the minimum speed possible at full torque [25]. Two methods of vector control are serviceable: direct field oriented control (DFOC) and sensor (indirect) field oriented control (IFOC) that is used more often, as these drives are easier to operate over the entire speed ranging from zero to high speeds in closed loop mode. In the case of feedback vector control, feedback signals that represent angle and magnitude are calculated directly with use of current or voltage model. In the case of direct-coupled control, the flux magnitude feedback and space angle signals in essence represent the stator current and rotor speed. Consequently, by summing the rotor angle they obtain their intrinsic flux space angle that corresponds to the rotor speed and the determined slip angle reference value corresponding to the slip frequency [26]. IMs sensorless control is desirable in terms of reliability and price. Pre-requisitions for the sensorless control comprise acquiring information about rotor speed from the measured stator electric current and voltage that is combined with open-loop estimates or closed-loop observers [27]. The software tools for the nonlinear control systems development has enabled many opportunities for ongoing progress of control systems design.