# Continuous Control Set Predictive Current Control for Induction Machine
## 1 Introduction  
Induction machines are crucial part of today's world industry because of their robustness and power per volume. Thanks to the research in the control field, they achieve satisfying reference tracking and can easily replace DC machines. Methods that revolutionized the field of induction machine control are field oriented control (_FOC_), developed in the seventies by [PERSON] and [PERSON] which are presented in their Ph.D. thesis [1, 2] and direct torque control (_DTC_), developed in the eighties by [PERSON] and [PERSON] [3]. From there, field of research for induction machine control expanded and many more authors contributed to the progress and countless variations of the methods emerged. At the time, model predictive control (_MPC_) was used in slow chemical processes, due to high computational burden that computers could not handle, but, with the development of digital signal processors, these methods could slowly be implemented to control fast processes. Authors [PERSON] et al. made a nice overview of the subject in their review paper [4], where they classified different finite and continuous control set methods. Extended classification of the _MPC_ can be found in [5]. Application of finite control set _MPC_ in different types of power converters is shown in papers [6] by [PERSON] et al. and [7] by [PERSON] et al. From these papers, one important note can be concluded, which is that plants can be controlled using _MPC_ by finite or continuous command control sets. Since the fields of power electronics and drives use discrete switching of the converters to control the plants, any of those two methods can be utilized. In the field of _MPC_ for induction machines, two distinct methods can be recognized: predictive torque control (_PTC_) and predictive current control (_PCC_). There is abundance of important comparison papers that investigate these methods and compare them to classical methods. Authors [PERSON] et al. made a comparison of _FOC_, _DTC_, _PCC_, and _PTC_ in [8], while authors [PERSON] et al. contributed with comprehensive comparisons of _FOC_, _DTC_, and _PTC_ in [9]. Authors [PERSON] et al. compared _FOC_ and _PTC_in [10], while [PERSON] et al. made a comparison of _PTC_ with _PCC_ and _DTC_ in papers [11; 12]. A lot of papers emerged with the attempts to improve upon the existing induction machine _MPC_ methods. Authors [PERSON] et al. developed a method for optimal setpoint calculation for the _PTC_ in [13]. It is known that in _PTC_, a weighing factor must exist in the cost function in order to penalize torque and flux errors. Authors of [14; 15] improve the methods to eliminate the weighing factor calculation. Authors of [16; 17; 18], took interesting approaches to further optimize the method where the switch-on on time of the optimal voltage vector is calculated, so that the torque ripple is minimized. There is much more content on _PTC_ that a reader is referred to in papers such as [19], where authors use combination of Kalman filter and standard _PTC_ for current and flux estimation, and [20], where authors improve the performance of the _PTC_ by deriving an algorithm for state estimation at longer predictive horizon. Regarding _PCC_, a lot of papers are published where authors improve upon existing methods. Authors [PERSON] et al. use universal proportional integral observer instead of PI speed regulator in [21] to improve the load torque disturbance rejection and in [22] they modify it to deal with parameter uncertainties. Authors of [23] improve the _PCC_ for low sampling time controllers by adjusting the discrete predicting plant model. Authors [PERSON] et al. improved upon the method by replacing the conventional speed PI controller with extended high-gain state observer in [24] and Luenberger observer in [25] to enable encoderless operation. All of these methods are based on the finite control set _MPC_, that commands variable switching frequency to the converter, which increases the risk of resonance and torque ripple on the machine.