劉 康志

The phase-shaping technique is a vital element for the control design of parametric systems. However, how to extend the technique to the matrix case is still an unsolved problem because we lack an easily applicable characterization of phase angle for transfer matrices. This article tackles this problem based on a model called the sectorial ball. Phase shaping is carried out via a scope matrix, and the corresponding design conditions are established. Furthermore, a metaheuristic algorithm is tailored for the design. Then, it is shown in detail how to apply this phase-shaping algorithm to design a high-performance gain-scheduled controller for parametric systems as well as saturated systems. Finally, this method is applied to an electronic throttle system with input saturation. Experiments and comparisons with other saturation control methods validate the effectiveness of the proposed method.

Weight learning forms a basis for the machine learning and numerous algorithms have been adopted up to date. Most of the algorithms were either developed in the stochastic framework or aimed at minimization of loss or regret functions. Asymptotic convergence of weight learning, vital for good output prediction, was seldom guaranteed for online applications. Since linear regression is the most fundamental component in machine learning, we focus on this model in this paper. Aiming at online applications, a deterministic analysis method is developed based on LaSalle's invariance principle. Convergence conditions are derived for both the first-order and the second-order learning algorithms, without resorting to any stochastic argument. Moreover, the deterministic approach makes it easy to analyze the noise influence. Specifically, adaptive hyperparameters are derived in this framework and their tuning rules disclosed for the compensation of measurement noise. Comparison with four most popular algorithms validates that this approach has a higher learning capability and is quite promising in enhancing the weight learning performance.

Smart grid allows the penetration of a high percentage of power from renewable energy sources (RES). The intermittent nature of RES makes accurate prediction of its output power impossible, and the prediction uncertainty is inevitable. This imposes a great challenge to the operation of smart grid. This paper focuses on photovoltaic (PV) generation and proposes a robust stochastic approach for the grid operation. First, we show that the uncertainty can be significantly reduced by the smoothing effect of PVs and build a simplified statistical model for the prediction of the total PV power, together with a bound of prediction uncertainty. After that, a criterion for the frequency maintenance is derived, which relates the allowable bound of frequency deviation to that of the PV power uncertainty. Then, a robust stochastic economic dispatch of the thermal power is formulated based on this criterion. Further, we propose an optimal PV dispatch method based on a peak-cut operation to maximize the PV output while guaranteeing the frequency performance. Finally, the operation performance is analyzed in detail on an annual basis by simulations using actual solar radiation data. It is revealed that the frequency quality is maintained with a 5% increase in fuel cost and an 11% reduction of PV power for a penetration ratio over 30%, compared with the case w/o frequency maintenance.

Spatially cyclic disturbances exist widely in rotating machines. They usually have fixed spatial cycles rather than constant time periods, which affect the stationarity of angular speed tracking. An input matching least mean square (LMS) adaptive filter (IMLMS-AF) is proposed to cope with the effects of spatially cyclic disturbances. The IMLMS-AF sets a part of the inputs as spatially cyclic signals for disturbance rejection and forms another part as a time-dependent function for reference tracking. Furthermore, an updated law and convergence of the pending weights are given. The system's stability is proved by combining the instantaneous gradient with Lyapunov theory. Moreover, the IMLMS-AFs are parallelized to reject disturbance with multiple components and reference tracking. The effectiveness and superiority of the proposed control method are verified and compared with other methods by simulations and experiments.

In robust control problems, how to elicit and utilize the uncertainty information is the key in achieving a good robust performance. For passive uncertainties, the phase bound plays a fundamental role. For nonpassive uncertainties, the gain bound is used up to date. The former leads to the passivity approach and the later to the small-gain approach. A recently developed bounded positive real model succeeded in extracting both the phase and the gain information from passive uncertainties. However, it is still not known how to model the phase bound of a nonpassive uncertainty. Aiming at achieving an even higher performance for nonpassive uncertain systems, this article proposes a new model together with a modeling procedure for a class of nonpassive uncertainties. This model well captures both the gain and the phase features of the nonpassive uncertainty. Further, a numerically tractable design method is developed by extending the passivity method. The advantage of the proposed method is demonstrated through a real-world case study.

The robust performance design of parametric systems is a long-standing unsolved problem, even though its analysis has seen significant success. Most existing design methods usually treat the parameter uncertainty as other types, such as norm-bounded uncertainty, and apply the corresponding approach. However, such treatment inevitably broadens the range of uncertainty and brings about design conservatism consequentially. To overcome such difficulty and establish a less conservative performance design method for parametric systems, this article looks back at the passivity theory and put forward a phase-shaping approach. This approach is composed of a generalized Popov transformation and a phase-shaping method for the nominal system. The key idea is to transform an uncertain but positive parameter into a positive real function while shaping the phase of the nominal system via a meta-heuristic method. This design freedom of phase shaping makes it possible to achieve a higher performance. Furthermore, this method is applied to the control design of drivetrain system: a test bed for automobile drivetrains. Its superiority is validated experimentally on an industrial setup.