Command filtered adaptive fuzzy backstepping control method of uncertain non‐linear systems

Abstract

The command filtered adaptive fuzzy backstepping control method has been proposed in this study. By using the command filter, it is not only the states, the actuator constraints, and the problem of 'explosion of complexity' in conventional backstepping have been solved, but also the calculation of partial derivatives is unnecessary, so that control law and update law become succinct. Fuzzy logic systems, designed in this study, are utilised in real-time identification of the uncertain non-linear functions. Throughout the process of controller design, the transformed style and Butterworth low-pass filter are applied to solve the problem of unknown control directions. Using the Lyapunov theorem, it has been shown that the approach can guarantee all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, an application of the method has been made to the controller design of the attack angle of a hypersonic vehicle. The simulation results are given to prove the effectiveness of the method presented in this study. IntroductionIn the past few years, adaptive fuzzy backstepping method has made much progress and became one of the most popular robust and practical control methods for uncertain non-linear systems (see and references therein). Yang and Zhou [1] and Mohammad and Hamid [2] presented adaptive fuzzy backstepping methods for single input single output (SISO) systems. Sui et al. [3] and Xu et al. [4] proposed the fault-tolerant controllers by using adaptive fuzzy backstepping methods. To overcome unknown backlash-like hysteresis properties of the actuators and the time delay which are common in the control systems, Boulkroune et al. [5] and Shahnazi et al. [6] presented the stable adaptive fuzzy controllers for the interconnected uncertain non-linear systems. However, the approaches proposed in [5, 6] are limited to be suitable for the controlled plants which must satisfy matching conditions. Li et al. [7], motivated by the aforementioned literatures, presented an output-feedback control approach for time-delay systems. It is not only the unknown backlash-like hysteresis properties of the actuators has been taken into account, but also can be applied for the complicated systems whose states are not measured and that do not satisfy the matching conditions. It is known that the phenomenon of the physical saturation of the actuators, which often degrades the performance of the systems or even severely damages the stability, is inevitable in the controllers design process. The analysis and designations of the systems with input saturations have been well studied in [8, 23] and references therein. Li et al. [8] presented a direct adaptive fuzzy backstepping approach. The hyperbolic tangent and Nussbaum gain functions are applied effectively to handle the non-linearities aroused by the input saturations. Chen et al. [23] proposed the scheme to handle the unknown control directions. However, it requires some details of the systems. For example, the control coefficient ma...

Command Filter Backstepping Sliding Model Control for Lower-Limb Exoskeleton

“…To avoid the "explosion of complexity" in the controller design process, a second-order nonlinear command filter is employed in this paper. The command filter ensures that the desired command and its derivative satisfy the same magnitude and rate constrains [24].…”

“…By using the command filter, the analytical derivate is unnecessary and the "explosion of complexity" in the controller design process is avoided [24][25][26]. Besides, the problem mentioned in (ii) is solved.…”

Neural Network Dynamic Surface Backstepping Control for the Speed and Tension System of Reversible Cold Strip Rolling Mill

“…Furthermore, for the uncertainty item with relatively small value and change rate, a nonlinear disturbance observer (NDO) [12,13] can be adopted to conduct dynamic observation and compensation, because its structure is simple, calculation amount is small, and control parameters are easily set. On the other hand, for an uncertainty item with relatively large value and change rate, neural network control [14,15], fuzzy control [16,17], or fuzzy neural network control [18,19] can be adopted to conduct dynamic approximation and compensation, because they can approximate any continuous function online, which is helpful to improve the tracking control precision and the robust stability of the system. Therefore, in this paper, for the speed and tension system of reversible cold strip rolling mill with uncertainties, a control strategy is proposed based on nonlinear disturbance observers (NDOs), dynamic surface backstepping control, and neural network adaptive approximation.…”

Nonlinear Control of Back-to-Back VSC-HVDC System via Command-Filter Backstepping

“…But this kind of controller has the following two main disadvantages: (1) the derivative of each virtual controller needs to be analyzed and calculated, and the calculation process is very complicated, so it is difficult to be applied in practical engineering; (2) physical limitations in practical systems are not considered in the design process of controller, which may cause the problem of control saturation [14]. Currently, there are many ways to solve the above problems, such as dynamic surface control [23,24] and command filter [25,26]. Among them, command filter is a more effective method compared to the dynamic surface control, because the constraint of amplitude, rate, and bandwidth are introduced in the filter process of command filter, which is more convenient to modulate and limit the virtual control signal and the actual control signal to meet the actual control requirements.…”