PMSM System Reduced-Order Feedback Linearization for Independent Torque Control electrical projects


PMSM System in parallel to a 2-level 3-leg inverter gives a way to build up a high power-density driving system using existing electronic devices. But this type of system has a nature of nonlinearity that creates an obstacle in high performance control and the original system cannot be feedback-linearized directly.


This article presents a reduced-order feedback-linearization method. In the first place, an extra order-reducing step that separates the system as a main system and an auxiliary system is applied. Then a feedback-linearization method is applied to the reduced-order system. With these effort, the original system can be converted into a linear time-invariant system bringing the controller design problem into the linear domain.

Load torque

In the last step, a linear robust state-feedback controller is used to achieve the speed control as well as compensate the unmeasurable external load torque. An extensive experiment is given to verify the feasibility and good performance in a highly unbalanced load torque situation of the designed controller.


  1. Parallel PMSM
  2.  Robust control
  3.  Feedback-linearization



Figure 1. Proposed Controller Scheme.


Figure 2. Speed And _D Response Of Speed Command Experiment.

Figure 3. Current Response Of Speed Command Experiment.

Figure 4. Speed And _D Response Of _D Command Experiment.

Figure 5. Current Response Of _D Command Experiment.


In this article, we have presented a two-step state-feedback controller for the MIDPMSM system such that the two machines are carried out in closed-loop systems for handling the highly unbalanced load torque situation. This article proposes a new way to linearize a nonlinear system if feedback-linearization cannot be applied directly.


The major contribution can be summarized in three aspects. First of all, a state-space description for the MID PMSM system is set up, and it is an affine nonlinear system with unknown inputs. And then, the original affine nonlinear system is linearized through two steps: order reducing and state-feedback linearization. With these two steps, the controller design problem is brought into the LTI system domain.


Secondly, in the state-feedback linearization stage, the stability of the constrained two-dimensional subsystem (7) is fully considered and dealt with. Indeed, in order to keep its stability, the calculation of the disturbance compensation gain k is given by analyzing eigenvalue constraints through solving its characteristic polynomial. Thirdly, based on the reduced-order linearized system, a state feedback controller together with an integrator is designed.


In this way, both goals, closed-loop stability and reference tracking, are reached. The experiment also proves that an open-loop machine can have the risk of becoming unstable when the “master-slave” method is used. The proposed controller can avoid this situation by putting both machines under closed-loop control. Although the proposed controller design method has shown its great advantages, at least one drawback of the controller is also left. This controller can hardly handle the singularity point of the system, which creates an obstacle. How to overcome the drawback becomes one of our next considerations.


 [1] Z. Deng and X. Nian, “Robust control of two parallel-connected permanent magnet synchronous motors fed by a single inverter,” IET Power Electron., vol. 9, no. 15, pp. 2833_2845, Dec. 2016.

[2] J. M. Lazi, Z. Ibrahim, M. H. N. Talib, and R. Mustafa, “Dual motor drives for PMSM using average phase current technique,” in Proc. IEEE Int. Conf. Power Energy, Kuala Lumpur, Malaysia, Nov. 2010, pp. 786_790.

[3] A. A. A. Samat, D. Ishak, P. Saedin, and S. Iqbal, “Speed-sensorless control of parallel-connected PMSM fed by a single inverter using MRAS,” in Proc. IEEE Int. Power Eng. Optim. Conf., Melaka, Malaysia, Jun. 2012, pp. 35_39.

[4] A. Del Pizzo, D. Iannuzzi, and I. Spina, “High performance control technique for unbalanced operations of single-vsi dual-PM brushles motor drives,” in Proc. IEEE Int. Symp. Ind. Electron., Bari, Italy, Jul. 2010, pp. 1302_1307.

[5] J. M. Lazi, Z. Ibrahim, M. Sulaiman, I. W. Jamaludin, and M. Y. Lada, “Performance comparison of SVPWM and hysteresis current control for dual motor drives,” in Proc. IEEE Appl. Power Electron. Colloq. (IAPEC), Johor Bahru, Malaysia, Apr. 2011, pp. 75_80.

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