# New Stable Non-Vector Control Structure for Induction Motor Drive
## 1 Introduction  
Induction motors (IMs) are robust and reliable, and due to their low cost and maintenance, they find a wide utilization in industrial applications. A problem consists of their control requiring more complex control circuitry due to variable frequency, complex dynamics, and parameter variations [1, 2, 3]. The IM itself presents a typical example of a nonlinear and considerably oscillating system with incorporated positive feedback. The accuracy of its speed control is significantly influenced by unknown external disturbances and variable motor parameters. Several control methods of the IM are known. The simplest one is the scalar speed control method. It has a simple control structure [4, 5] due to which is suitable for simpler industrial applications. A better drive performance of the scalar control method requires using on account of a more expensive and less reliable solution. A precise drive performance is obtained by field oriented control (FOC) employing classical cascade PI controllers [6]. Various modifications of the FOC usually requiring transformation of the IM variables into a rotating reference frame have been developed which enable to control the IM in a similar manner like a separately excited DC motor [7, 8, 9]. A drawback of such a solution consists of increased complexity of the control schemeand in necessity of using powerful computational means (digital signal processors) for its implementation. From the point of view of the modeling and control the IM principally presents a nonlinear dynamic system with uncertain parameters. Many design techniques for nonlinear control have already been applied for the control of IM drives providing better performance than the FOC [10; 11]. Various sensorless methods to measure the rotor position of electrical drives with IMs [12; 13; 14] have been proposed in order to decrease the hardware complexity and cost and simultaneously to increase higher mechanical robustness and by this a reliability of the drive performance. From the field of applications of nonlinear control methods to the speed and position control of the IMs, a sliding mode control should be mentioned [15; 16; 17]. Soft computing methods like fuzzy logic, artificial neural networks, evolutionary algorithms and their combinations have also been applied for the IM drive's control [18; 19; 20; 21; 22; 23]. However, again, their drawbacks consists of powerful real-time calculation processes and, moreover, they can incline to the stability problems of the system (as is often the Z\(\backslash\)case of fuzzy control theory methods). An overview of several methods of the IM control at inaccurate determined parameters (the rotor resistance, mains failure and load torque) is given in [24]. It follows that the quality of the IM control depends in principle on the accuracy of the IM model used for all methods. However, the exact model of the drive is not available as at a large volume of production, the exact motor parameters can vary significantly. Several methods have been proposed to solve the problem of IM control with an inaccurate model. A disadvantage of an adaptive version of the sliding mode [25; 26] is that it guarantees the robustness only within a range of the uncertainties, and it still suffers from a chattering problem. The predictive control [27; 28; 29] can be complemented by a parameter observer to estimate the uncertain model parameters, but the stability for such schemes is usually not guaranteed. A backstepping control method [30], that has appeared recently, allows the design of the control law and the estimation of the motor parameters. However, the proposed method is suitable for a limited set of adaptive parameters only. Summarizing the review, it is clear that the high quality of the IM control should take into account the following criteria: a nonlinear and oscillating character of the IM dynamics, variations of motor parameters, the influence of external disturbances, and a simple implementation of the control algorithm.