Copyright © IFAC 12th Triennial World Congress, Sydney, Australia, 1993 A STABLE NONLINEAR OBSERVER DESIGN FOR PERMANENT-MAGNET SYNCHRONOUS MOTORS Kuan-Teck Chang*, Teck-Seng Low* and Tong-Heng Lee** *Magnetics Technology Centre, National University of Singapore, 10 Kent Ri£ige, Singapore 0511 **Department of Electrical Engineering, National University of Singapore, 10 Kent Ridge, Singapore 0511 Abstract The application of vector control techniques in ac drives demands accurate position and speed feedback information for the current control and servo control loops. This paper describes the design of a stable speed observer system suitable for use with the permanent-magnet synchronous motors (PMSM) as a software transducer. TIle observer is developed from the dq model of the machine. A technique employing state detection and eigenvalues confmement is used to achieve global stability and consistent convergency of the observer system. Key Words. Nonlinear Systems; Observers; Servomechanism; Motor Control; Observability. 1 BACKGROUND Advancements in magnetic materials, semiconductor switching devices and control strategies continue to enhance the popularity of the PMSM in drive applications. The rotor position is critically important in vector control of PMSM to facilitate the electronic commutation, and a position transducer has to be installed onto the machine. A common solution employed to obtain speed information is to estimate the speed from the position information using some recursive algorithms implemented on either software or hardware (Lorenz and Patten, 1991). Such recursive techniques has to sense the position in order to estimate the speed which results In an inherent lag in the estimation. wrid and wri q . As such the state model cannot be expressed in standard linear for clX / dt = AX + Bu, and the wealth in linear system theory cannot be utilized. An approach that could be used for the control and observation of such nonlincar system is by piecewise linearization technique. Another possible approach is the more recent feedback lineari7.ation technique which uses differential geometric approach to globally linearize the system [Isidori, 1989] by using the state feedback. However it is difficult to design a convergent observer for nonlinear systems using this approach, as pointed out in [Slotine and Li, 1991). 2.2 Nonlinear Observer De.fiigns 2 SPEED OBSERVER DESIGNS FOR PMSM In a PMSM system the currents of id and iq are measured using current transducers. With these a 2.1 PMSM Model transformation on system described by the equation (I) can be carried out as follows : The dynamic model for PMSM in the dq- transformed rotor reference frame (Krause, 1987) is given in state-space form by equations (1) and (2): d{iq] [-RlL 0 0 0 IV q ] d Id = 0 -RI L Iq 'd 0 V L 0 Vd "¥ a1J 0 -l3/J "¥ 0 0 -N/J 1i. (3) d{"] [-RlL 0 -)JLII']1- w ,tdIIIL 0 0 IV q ] d 'd = 0 -RI L 0 'd "it, 0 ilL 0 Vd w,. aV 0 -8/J w,. 0 0 0 -N/J 1J. dB, / dt (I) where id o and i q O are the detected direct-axis and quadrature-axis currents. The measurement matrix y (2) is the linear combination of currents: The state-space model in (1) contains nonlinearities in the cross-product forms of two state variables, 137 y = [I I 0 ][i q id w, r (4)