Theoretical Proof Of Stability Research Articles

Adaptive Finite-Time Control on SE(3) for Spacecraft Final Proximity Maneuvers with Input Quantization

In this paper, a bounded finite-time control strategy is developed for the final proximity maneuver of spacecraft rendezvous and docking exposed to external disturbance and input quantization. To realize the integrated control for spacecraft final proximity operation, the coupling kinematics and dynamics of attitude and position are modeled by feat of Lie group SE 3 . With a view to improving the convergence rate and reducing the chattering, an adaptive finite-time controller is proposed for the error tracking system with one-step theoretical proof of stability. Meanwhile, the hysteresis logarithmic quantizer is implemented to effectively reduce the frequency of data transmission and the quantization errors are reduced under the proposed controller. The algorithms outlined above are based on an integrated model expressed by SE 3 and denoted by uniform motion states, which can simplify the design progress and improve control precision. Finally, simulations are provided to exhibit the effectiveness and advantages of the designed strategy.

Direct torque control for cable conduit mechanisms for the robotic foot for footwear testing

As the shoe durability is affected directly by the dynamic force/pressure between the shoe and its working environments (i.e., the contact ground and the human foot), a footwear testing system should replicate correctly this interaction force profile during gait cycles. Thus, in developing a robotic foot for footwear testing, it is important to power multiple foot joints and to control their output torque to produce correct dynamic effects on footwear. The cable conduit mechanism (CCM) offers great advantages for designing this robotic foot. It not only eliminates the cumbersome actuators and significant inertial effects from the fast-moving robotic foot but also allows a large amount of energy/force to be transmitted/propagated to the compact robotic foot. However, CCMs cause nonlinearities and hysteresis effects to the system performance. Recent studies on CCMs and hysteresis systems mostly addressed the position control. This paper introduces a new approach for modelling the torque transmission and controlling the output torque of a pair of CCMs, which are used to actuate the robotic foot for footwear testing. The proximal torque is used as the input signal for the Bouc–Wen hysteresis model to portray the torque transmission profile while a new robust adaptive control scheme is developed to online estimate and compensate for the nonlinearities and hysteresis effects. Both theoretical proof of stability and experimental validation of the new torque controller have been carried out and reported in this paper. Control experiments of other closed-loop control algorithms have been also conducted to compare their performance with the new controller effectiveness. Qualitative and quantitative results show that the new control approach significantly enhances the torque tracking performance for the system preceded by CCMs.

Control and Stability Analysis of Modular Multilevel Converter Under Low-Frequency Operation

The modular multilevel converter (MMC) is increasingly becoming popular for multi-MW drive systems. One of the main technical challenges associated with the operation of MMC for adjustable-speed drives is the large magnitude of submodule (SM) capacitor voltage ripple under constant-torque low-speed operation. This paper proposes two new control strategies to reduce the magnitude of the SM capacitor voltage ripple in the MMC-based adjustable-speed drive systems under constant-torque low-speed operation. The proposed control strategies are based on injecting a square-wave common-mode voltage at the ac-side and a circulating current within the phase-legs to attenuate the low-frequency components of the SM capacitor voltages. The frequency spectrum of the injected circulating current consists of components in the vicinity of either the common-mode frequency or the common-mode frequency and third harmonic of the common-mode frequency. This paper also provides: i) a theoretical comparison of the proposed control strategies with the existing ones; ii) a controller design methodology to systematically determine the controller gains of the proposed control strategies; and iii) a theoretical proof of stability of the proposed control strategies and their design methodology based on Lyapunov analysis of singularly perturbed nonlinear non-autonomous systems. A set of experimental results for various case studies on a laboratory-scale prototype are provided to support the theoretical proof of stability of the proposed control strategies and their design methodology, and to show the superior performance of the proposed strategies over the existing strategy.

Robust sliding mode control for spacecraft global fast-tracking manoeuvre

This article studies spacecraft attitude control problem to achieve global fast tracking for ground target. The expected spacecraft attitude parameters and a Lagrange-like model of spacecraft attitude motion are presented, respectively, and then a robust sliding mode controller based on this model and Euler parameters is designed to achieve tracking in the presence of model uncertainties and external disturbances. The proposed controller can guarantee global fast stability of the closed-loop systems and convergence of tracking errors by employing global fast-sliding mode model, which combines the advantages of linear and terminal sliding mode controls. The theoretical proof of stability and convergence is given subsequently. Numerical simulations are finally presented to demonstrate the performance of the developed controller.

Application of fuzzy neural network controller in hydropower generator unit

PurposeThe purpose of this paper is to develop a new hybridized controller based on fuzzy reasoning and neural network (NN) for hydropower generator unit (HGU).Design/methodology/approachThe approach contains fuzzy neural networks controller (FNNC), RBF network identification (RBFNI) and HGU system. FNNC may give control value to control HGU via fuzzy NN reasoning and computing according to HGU rotate speed error and error varying rate. RBFNI is used to identify the character of HGU system and predict its output. FNNC may adjust parameters and member function according to the identifying and predictive outcome of RBFNI.FindingsSees that the hybridized control system is feasible and stable, and the controlling performance of the hybridized system is superior to conventional fuzzy controller.Research limitations/implicationsThe theoretical proof of stability of the proposed scheme still remains to be studied. Accessibility and availability of membership functions and control rules is also a limitation applied.Practical implicationsThe main advantage of the proposed method is that FNNC has reasoning, learning, and optimizing capability which can control effectively HGU. This will be useful for control engineers to control complex industrial plants.Originality/valueThe paper proposes new combined approach to optimal control of HGU using FNNC, and it is aimed at operational researches and engineers, especially those who dealt with HUG controller.

Stability of Cascaded Fuzzy Systems and Observers

A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models with linear or affine consequents. It is well known that the stability of these consequent models does not ensure the stability of the overall fuzzy system. Therefore, several stability conditions have been developed for TS fuzzy systems. We study a special class of nonlinear dynamic systems that can be decomposed into cascaded subsystems, which are represented as TS fuzzy models. We analyze the stability of the overall TS system based on the stability of the subsystems and prove that the stability of the subsystems implies the stability of the overall system. The main benefit of this approach is that it relaxes the conditions imposed when the system is globally analyzed, thereby solving some of the feasibility problems. Another benefit is that by using this approach, the dimension of the associated linear matrix inequality (LMI) problem can be reduced. For naturally distributed applications, such as multiagent systems, the construction and tuning of a centralized observer may not be feasible. Therefore, we also extend the cascaded approach to the observer design and use fuzzy observers to individually estimate the states of these subsystems. A theoretical proof of stability and simulation examples are presented. The results show that the distributed observer achieves the same performance as the centralized one, while leading to increased modularity, reduced complexity, lower computational costs, and easier tuning. Applications of such cascaded systems include multiagent systems, distributed process control, and hierarchical large-scale systems.

A predictive control scheme based on neural networks

Purpose – To develop a new predictive control scheme based on neural networks for linear and non‐linear dynamical systems.Design/methodology/approach – The approach relies on three different multilayer neural networks using input‐output information with delays. One NN is used to identify the process under control, the other is used to predict the future values of the control error and finally the third one is used to compute the magnitude of the control input to be applied to the plant.Findings – This scheme has been tested by controlling discrete‐time SISO and MIMO processes already known in the control literature and the results have been compared with other control approaches with no predictive effects. Transient behavior of the new algorithm, as well as the steady state one, are observed and analyzed in each case studied. Also, online and offline neural network training are compared for the proposed scheme.Research limitations/implications – The theoretical proof of stability of the proposed scheme st...