# New Stable Non-Vector Control Structure for Induction Motor Drive
## 8 Discussion  
Based on the simulation and experimental results and on comparison of the designed control structure with the vector control structure, the proposed new control structure with the reference model is characterized by the following properties:  
* In general, the order of the reference model must be the same one as the order of the controlled system. In practice, it is often possible to reduce the controlled system order (e.g., in the case of electrical machines, the influence of fast control loops can be neglected, the dynamics of electromagnetic phenomena can also be replaced by the 1 st order system, etc.). In the case of the IM, the number of the reference model state variables has been the same as the order of the reduced controlled system. The reference model of the IM presents a nonlinear 2 nd order system (Figure 3). This significantly simplifies the control structure while maintaining its required properties which has been proved by the simulation on the 3 rd order IM model and by experimentation on a real drive with IM (Sections 5 and 7). * For the new control structure, no accurate values of the controlled system parameters are required. This fact is described in Section 6, where the influence of an unknown change of the motor important parameters (\(R_{2}\), \(J\)) on the dynamics is shown in Figures 11-13 and compared performance of the designed control structure and vector control structure. This fact is shown and described in more detail in Section 6, where the influence of the unknown change of important parameters (\(R_{2}\), \(J\)) on the control dynamics of the designed and vector control structures are compared in Figures 11-13. * The parameter's setting is performed through two constant parameters (the gains). The first parameter (the parameter \(\alpha\) in the description of the reference model (23)) determines the overall control dynamics. It can be determined from the measured standardized responses of the controlled system (e.g., based on unit step characteristics, Figure 2) using the Shanon-Kotelnik theorem. The elements of the vector \(\mathbf{k}^{T}\) that ensure the transient phenomena and stability present further optional parameters. They must comply with condition (16). The setting of the mentioned parameters can be realized without any exact knowledge of the controlled nonlinear system parameters. They must be positive and are tuned by a gradual increase of their values up to physical limitations of the controlled system, i.e., up to the current limitation of the IM. * Comparing with the speed vector control structure, the proposed control structure is a simpler one that concerns the interconnection and lower order of the control structure). The use of the necessary Park transform in the proposed control structureis independent from the exact knowledge of the IM parameters which increases the quality of control (as shown in Section 6). * From the view of the superior control, the novel structure exhibits dynamic properties of an optimal linear dynamic system satisfying the criteria of minimum control deviation and minimum input energy [32]. Thus the drive properties are practically identical to the properties of a high quality vector control of the IM drive. * In the proposed control structure, the controlled nonlinear system is complemented by linear subsystems only (Figure 8a). For this reason, it can be implemented by cheap conventional hardware. * The stability of the proposed control structure is ensured by calculating the parameters (the elements of the positive definite matrix **P**) by means of the Lyapunov matrix Equation (11) or in the case of an optimal chosen model according to [32], they can be calculated from (27). * The proposed control structure is robust against considerable variations changes not only of the important parameters of IM (e.g., of the rotor resistance \(R_{2}\) (Figure 6) or of the moment of inertia--Figure 7a,b), but also to inaccurate known parameters of the nonlinear controlled system.