On the basis of a novel dynamic model obtained under a special non-linear co-ordinate transform on a d}q-axis model (w.r.t. the stationary reference frame) of an induction motor, a simple but e!ective control law for speed regulation is proposed in this paper. This controller is designed using the concept of the "eld orientation and the property of linear PI-controller, and is shown to be robust with respect to variation of system parameters and load structure. To be rigorous, a Lyapunov theorem with a simple iterative criterion derived in this paper proves the local exponential stability of the system around any desired speed. Numerical simulations are also given to show the e!ectiveness of the presented control law.

In this paper, new and simple algebraic criteria are derived via elementary proofs to provide easy sufficient conditions for the standard absolute stability problems of nonlinear systems, i.e. Lur'e problems. These criteria are equivalent to the famous graphical circle criteria and Popov criterion. By means of the Sturm theorem and the Euclidean division algorithm, a Routh-Hurwitz-like Sturm criterion is obtained. No graphical technique is needed. Only basic numerical manipulations are involved in the new criteria. KEY WORDS Algebraic criteria Absolute stability Sturm theorem Q ( s ) = r i ' s d ( s ) + k-'d(s) + (1 + sd)n(s), P ( s ) = d ( s ) + r2s[k-'d(s) + (1 + d ) n ( s ) ] , rl E (0,001 r2 E [0, 00)

A sin ple control law for speed regulation of induction motor is proposed in this paper. This controller is designed based on the concept of the field orientation and the property of linear PI-controller, and is shown to be rot.*.t with respect to variation of system parameters and load strnctrrre. In fact, the local exponential stability of the system around any desired speed can be proved by a simple iterative criterion derived in this paper. Numerical simulations are also given to show the effectiveness of the presented control law. Nomenclature q-(d-)oxis stator current q-(d-)axis input stator voltage q-(d-)axis stator f 1112 rotor speed electromagnetic torque mechanical load torque ststor ( r o f o r ) resistance stator (rotor) inductance mtitual inductance nuniber of poles inertia of the rotor (LSL? -L:n)