Vector control methods for induction machines: an overview <s> IV. THE TORQUE EQUATIONS <s> The uniqueness of the constant control for the torque-transfer function (CCTTF) is discussed. The CCTTF has been developed for high-performance induction motor drives with a current controlled source. Two regions are discussed: the constant field region and the field weakening region. In the constant field region, two control schemes, vector control (VC) and a field acceleration method, have already been presented. However, in order to realize CCTTF, only VC is possible. In the field weakening region, the generation of the transient torque which disturbs CCTTF is inevitable. It is proved that there exists a unique way of minimizing the transient component, and such a control is proposed. > <s> BIB001 </s> Vector control methods for induction machines: an overview <s> IV. THE TORQUE EQUATIONS <s> The field acceleration method (FAM) and the indirect field-oriented control (FOC) for current-fed induction machines are theoretically compared, and their block diagrams are analyzed. It is shown that the indirect FOC and the T-1 type FAM are exactly the same. Moreover, the equivalence between the spiral vector used in FAM and the space vector used in FOC is demonstrated. The FOC theory explains the direct FOC, where an estimation of a direct measurement of the rotor flux is done. This direct scheme allows independent control loops for flux and torque, and thus can be considered more general than the FAM or the indirect FOC. > <s> BIB002
Torque is the most important variable in the control of electric-mechanical systems. It makes the connection of the mechanical and electrical parts. Equation (3) presents the electrical torque as the product of a reference flux and the stator current component orthogonal to it. This equation is similar to the one for a separately excited DC machine. In this paper the control methods based on this equation will be called "quadrature control methods." On the other hand, using (1) and (2), it is possible to write as a function of . Substituting this expression for in (3), it follows: BIB002 This expression presents the torque as a nonlinear and dynamic function of the slip frequency . The control methods based on this equation will be called "slip control methods." If the derivative terms are neglected, i.e., steady-state or quasi-steady-state conditions are assumed, the torque equation, for constant flux, shows an approximately direct relationship between torque and slip. As can be expected, with this approach a linear control can not produce the best dynamic behavior. However, when the rotor flux is chosen as the reference, then and (5) below can be obtained from BIB002 . In this case (5) is always exact even under transient conditions. These observations are also in accordance with the comments presented by Ueda et al. in BIB001 (5) V. QUADRATURE CONTROL METHODS As mentioned, these control methods are based on (3). They can be further subdivided into direct and indirect methods. Di- rect methods have a control loop for the flux and, therefore, a flux estimator or flux sensors are necessary. Indirect methods assume that the flux amplitude is constant, and its spacial position can be obtained with a feedforward block that has as an input of speed. Clearly, indirect methods are easier to implement but less accurate.