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Most subspace identification methods are developed for linear time-invariant system. However, in reality, most systems are time-varying. Hence the recursive version of subspace identification methods is urgently desired. In this paper, we propose a unifying framework of recursive subspace model identification algorithm, which is based on the orthogonal projection and principal component analysis (PCA). Based on our framework, the bona fide recursive algorithm is applied to update the QR factorization. Two recursive subspace model identification algorithms are developed for open loop and closed loop condition, respectively. The numerical simulations demonstrate the efficiency of the two algorithms comparing with other algorithms.

Firstly, the improved quadratic regression orthogonal design method is proposed. Secondly, the indoor physical experiment is carried out on the main affecting factors for the permanent magnet constant voltage device for vehicle application, and meanwhile, the corresponding output voltage and current mathematical model is established by means of the statistical analysis, mathematical model establishment. Finally, the influence mechanism of the different speed and frequency on the output voltage and current is analyzed. This research can provide an important basis for study of the permanent magnet constant voltage device.