Induction Motor Control Design

In this chapter we explore the advantages of feedback control assuming that all the state variables are measurable. This is not a realistic assumption since the rotor variables are usually not measured but it allows us to explore fully the potentiality of feedback control. In Section 2.1 we establish that the feedforward control does not guarantee the asymptotic stability of the desired operating point for every initial condition and for every parameter value: the load torque in particular is a critical parameter. Hence, feedback control is needed to achieve the asymptotic stability of the desired operating condition, for any load torque and for any initial condition. Six feedback control algorithms are then presented. The most complex is the dynamic feedback linearizing control presented in the last Section 2.6, which imposes an arbitrary linear dynamic behavior to the controlled motor. The input–output feedback linearizing control is presented in Section 2.4: it achieves arbitrary and decoupled linear dynamics for the two tracking errors of rotor speed and flux modulus; it is generalized in Section 2.5 by an adaptive input–output feedback linearizing control which identifies both the load torque and the rotor resistance in realistic operating conditions. The identification of these two parameters allows computation online of the optimal value of the rotor flux modulus which minimizes the power losses. All three feedback linearizing control schemes have excellent performances provided that the initial errors are sufficiently small: this is a significant limitation which is removed by the global control with arbitrary rate of convergence presented in Section 2.7. It is the evolution of the historically important direct field-oriented control which is presented in Section 2.2 and its variant, the indirect field-oriented control, which is discussed in Section 2.3 and can operate from any initial conditions. The field-oriented controls constitute a modification of the feedforward control discussed in Section 2.1 and contain the key steps to design the global control with arbitrary rate of convergence, which can operate from any motor initial conditions. The indirect field-oriented control is tested by experiments in Section 2.8 and its robustness with respect to rotor resistance variations is explored.

Under the assumption that the rotor speed, the stator currents, and the stator voltages are available from measurements, this chapter is devoted to the design of rotor flux (or rotor current) asymptotic observers and their adaptive versions when the rotor resistance is uncertain. Load torque estimators are also designed which can be used in conjunction with the flux observers. The estimation algorithms which are presented and analyzed in this chapter are intended to complement the control algorithms which were obtained in Chapter 2 under the assumption that the rotor fluxes are available for feedback and that the load torque and the rotor/stator resistances are known. The rotor fluxes have been shown to be observable in Chapter 1 so that global rotor flux observers with arbitrary exponential rate of convergence are designed in this chapter. Adaptive observers show that the rotor resistance can be estimated online along with rotor fluxes, provided that persistency of excitation conditions are satisfied.

In this chapter the state feedback controls presented in Chapter 2 and, in particular, the control given in Section 2.7 are combined with the rotor flux observers presented in Chapter 3: the goal is to obtain global output feedback controls which do not require flux measurements and guarantee rotor speed tracking for any initial condition of the motor. In Section 4.1 the global control with arbitrary rate of convergence which was presented in Section 2.7 is modified to eliminate the need of rotor flux measurements, at the expense of the property of arbitrary exponential rate of convergence. In order to recover this important property, in Section 4.2 the global state feedback control with arbitrary rate of convergence, discussed in Section 2.7, is modified so that the rotor fluxes can be replaced by the estimates provided by the rotor flux observer with arbitrary rate of convergence given in Section 3.1: the resulting observer-based global controller guarantees exponential convergence with arbitrary rate of both the tracking and the estimation errors. In Section 4.3 the control algorithm presented in Section 4.2 is made adaptive with respect to an uncertain load torque by incorporating the load torque estimator presented in Section 3.3. Finally, in Section 4.4 a global output feedback control algorithm is presented which is adaptive with respect to both the unknown load torque and the uncertain rotor resistance and achieves asymptotic rotor speed tracking. Under persistency of excitation conditions, exponentially converging estimates of the unmeasured rotor fluxes and of the uncertain parameters are obtained, while exponential tracking of rotor speed and flux modulus is achieved from any motor initial condition.

In this book the problem of designing a control for an induction motor has been systematically studied and thoroughly discussed using tools from nonlinear system theory, both for analysis and control purposes. Adaptive control techniques have been used to identify online critical parameters.