A Resolver-to-Digital Conversion Method Based on Third-Order Rational Fraction Polynomial Approximation for PMSM Control

Abstract

In this paper, a cost-effective and highly accurate resolver-to-digital conversion (RDC) method is presented. The core of the idea is to apply a third-order rational fraction polynomial approximation (TRFPA) for the conversion of sinusoidal signals into the pseudo linear signals, which are extended to the range 0-360° in four quadrants. Then, the polynomial least squares method (PLSM) is used to achieve compensation to acquire the final angles. The presented method shows better performance in terms of accuracy and rapidity compared with the commercial available techniques in simulation results. This paper describes the implementation details of the proposed method and the way to incorporate it in digital signal processor (DSP) based permanent magnet synchronous motor (PMSM) drive system. Experimental tests under different conditions are carried out to verify the effectiveness for the proposed method. The obtained maximum error is about 0.0014° over 0-360°, which can usually be ignored in most industrial applications.

Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises

“…In Theorem 1, the input-to-state stability in probability for the estimation error system (25) is guaranteed by the condition in terms of PDLMIs. The evolution of estimation errors is characterized by (26), where 1 ( ‖ ‖ x (l)‖ ‖∞ ) + 2 (‖v‖ ∞ ) denotes the upper bound of sample trajectories and 1 − represents the possibility that sample trajectories are bounded as t → ∞. It is readily seen from (26) that the upper bound of sample trajectories of estimation errors has close relationship with the upper bound of system state x (l) (t) and unknown but bounded noises v(t).…”

“…In recent years, there have been a number of results on the filter design of nonlinear polynomial systems. 12,[22][23][24][25][26] Compared with the existing literature, the distinctive novelties of this article lie in: (a) a novel polynomial filter design method is proposed under the less conservative condition; (b) the NSDS addressed is more complicated where state-and UBB disturbance-dependent noises are taken into account; and (c) the polynomial matrix inx of the filter is derived by solving PDLMIs via the SOS approach.…”

“…In recent years, much research attention has been devoted to the filtering and control problems of nonlinear polynomial systems (NPSs), which may represent a large class of nonlinear systems. 12,[21][22][23][24][25][26][27][28] For instance, the problems of H ∞ filtering and least squares filtering were investigated for the discrete-time NPSs in References 22 and 24, respectively. In the continuous-time case, the linear and polynomial H ∞ filters were respectively designed in References 25 and 23 for NPSs by means of the sum-of-squares (SOS) approach, and the problem of distributed H ∞ filtering was studied in Reference 12 for polynomial NSDSs over sensor networks.…”

“…In the continuous-time case, the linear and polynomial H ∞ filters were respectively designed in References 25 and 23 for NPSs by means of the sum-of-squares (SOS) approach, and the problem of distributed H ∞ filtering was studied in Reference 12 for polynomial NSDSs over sensor networks. In most existing literature on continuous-time polynomial filtering issues, 12,23,25,26 the asymptotical stability should be ensured for an augmented system without external disturbance, where the augmented state contains system state and estimation of state (or estimation error). Such a condition leads to much conservative since it requires that the original nominal system is asymptotically stable, then some less conservative ones should be provided for the filter design of NPSs.…”

A Novel Technique for Resolver-to-Digital Conversion Using Principal Frequency Component S-Transform

“…CORDIC (Coordinate Rotation Digital Computer) algorithm is another method suitable for fast calculation of trigonometric functions and suitable for the FPGA implementation [8]. However, the accuracy of the CORDIC algorithm is mainly affected by the limited number of iterations for microcontroller, mentioned in [9], and it is a challenge for general developers to have experience in developing special chips.…”