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The barrier Lyapunov function (BLF) and its variants such as the asymmetric barrier Lyapunov function (ABLF) combined with backstepping technique have recently been employed to handle constraints for a class of non-linear systems. However, the repeated differentiation in backstepping will result in the requirement of high-order differentiability and the complexity of controllers in the multiple-state high-order systems. This study introduces dynamic surface control (DSC) to deal with these problems. The authors propose a backstepping DSC scheme based on the ABLF to address time-varying output constraints for a class of non-linear systems. The proposed control scheme can avoid the proliferation and singularity of repeated differentiation. As a consequence, it can relax the requirements of high-order differentiability for stabilising functions and high power of output tracking error transformation involved in ABLF synthesis. The new controller can be proved to guarantee that all the closed-loop signals remain bounded, and to ensure output constraints never violated. Comparison studies with previous work validate that DSC incorporated with ABLF can achieve favourable performance bounded within constraints, and it can also ensure fast and stable tracking convergence in the presence of disturbance. Experimental results illustrate the effectiveness of the presented method. IntroductionIn practice, it is important to take account of constraints or limits, which may stem from physical constraints and performance requirements. During the operation, the violation of constraints may degrade performance, endanger the system, or even damage the hardware. To deal with the constraints or limits in the operation space and hardware capacity, constrained control become one of the emphasis areas in control theory and engineering study to enhance the performance and stability of real systems. Considerable research has been carried out to study problems of constrained control [1][2][3]. In [4,5], a method based on the notions of the set invariance has been investigated to handle input and state constraints; however, the constraints can be satisfied if and only if the initial state is constrained inside an invariant set. Reference governor was proposed to enforce fulfilment of the constraints [6-9] for a class of non-linear systems with uncertainties, where the state and control constraints can be specified for each specification by modifying reference signals supplied to the closed-loop systems. Model predictive control has also been well studied to cope with hard constraints on state and control variables [10,11], which required an online solution in a reasonable time for the optimal control problems. Different from the mentioned methods, the barrier Lyapunov function (BLF) [12] and its variants such as the asymmetric barrier Lyapunov function (ABLF) have recently been used to deal with state and output constraints for non-linear systems in the Brunovsky form with no need for explicit solutions of the systems. Unlike the original Ly...

As an important ancillary service for smart grid, voltage support has the capability to improve the grid condition when grid voltage unbalanced fault occurs. Several solutions, taking into account not only the root mean square voltage, but also the shape of the voltage fault, have been proposed. In particular, the control scheme proposed in this study introduces two contributions: a novel reference generator for voltage support and a new current tracking controller. Taking into account of the shape of the grid voltage, this reference generator has the capacity to increase the positive sequence fundamental voltage magnitude and decrease the negative sequence fundamental voltage magnitude, which improves the grid condition when unbalanced fault and voltage sags occur. Compared with other works, phase locked loop is eliminated in this generator which simplifies the structure of the controller. On the basis of output regulation theory, a simple-structure current tracking controller is proposed, which has a zero steady error under arbitrary order (or their combination) grid voltage harmonic disturbance. Simulations and experiments have verified the proposed control scheme.

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As an important device of the aircraft landing system, the antilock braking system (ABS) has a function to avoid aircraft wheels self-locking. To deal with the strong nonlinear characteristics, complex nonlinear control schemes are applied in ABS. However, none of existing control schemes focus on the braking operating status, which directly reflects wheels self-locking degree. In this paper, the braking operating status region is divided into three regions: the healthy region, the light slip region, and the deep slip region. An ABLF-based wheel slip controller is proposed for ABS to constrain the braking system operating status in the healthy region and the light slip region. Therefore the ABS will be prevented from operating in the deep slip region. Under the proposed control scheme, self-locking is avoided completely and zero steady state error tracking of the wheel optimal slip ratio is implemented. The Hardware-In-Loop (HIL) experiments have validated the effectiveness of the proposed controller.

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