Variable Structure Adaptive Backstepping Controller for plants with arbitrary relative degree based on modular design

Recently, variable structure design (VSD) has been intensively researched in the literature of model reference adaptive control (MRAC) for its well-behaved transient response and appealing tracking performance. In the recent work by Hsu [6], parameter switching mechanism has been introduced in the design of model reference controller to obtain better transient behavior. By taking a different viewpoint, we apply VSD to the control channel, and develop a new robust model reference adaptive controller for a class of uncertain plants with arbitrary relative degree. It is shown that in the presence of additive, multiplicative unmodeled dynamics, and bounded disturbance, the output tracking error can still be guaranteed to converge to zero with an exponential rate. Since the parameter update law is introduced in the synthesis of this new adaptive control law, the magnitude of the switching control forces can be reduced to a more realistic level for implementation. To highlight the improved performance, simulation results are conducted with an uncertain plant with relative degree two.

In this paper, we introduce a direct fractional order adaptive control design based on model reference adaptive control (MRAC) structure for a class of commensurate fractional order linear systems with an arbitrary relative degree, and whose parameters are unknown. By generalising the application of standard direct MRAC strategy to plants described by fractional order models, we develop a fractional adaptive control scheme (FOMRAC) based on the output feedback. We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory. The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem. Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.

In this paper an adaptive backstepping control system is proposed to control the rotor position of a permanent magnet synchronous motor (PMSM) drive using recurrent fuzzy neural network (RFNN). First, the field-oriented mechanism is applied to formulate the dynamic equation of the PMSM servo drive. Then, an adaptive backstepping approach is proposed to compensate the uncertainties in the motion control system. With the proposed adaptive backstepping control system, the rotor position of the PMSM drive possesses the advantages of good transient control performance and robustness to uncertainties for the tracking of periodic reference trajectories. Moreover, to further increase the robustness of the PMSM drive, a RFNN uncertainty observer is proposed to estimate the required lumped uncertainty in the adaptive backstepping control system. In addition, an on-line parameter training methodology, which is derived using the gradient descent method, is proposed to increase the learning capability of the RFNN. The effectiveness of the proposed control scheme is verified by experimental results.

Variable structure adaptive fuzzy control for a class of nonlinear time-delay systems

The problem of variable structure adaptive fuzzy control for a class of nonlinear time delay systems is investigated. Sliding surface dependent of the time delay is constructed based on the Lyapunov-Krasovskii method. Two adaptive fuzzy logic systems are proposed to approximate two unknown continuous nonlinear functions containing the current state and the delayed state respectively. The corresponding reaching law is designed, which can drive the state trajectory of the closed-system onto the sliding surface within limited time.

Designing an adequate controller for a plant with an arbitrary relative degree is still an active area of research. In this paper, a discrete variable structure model reference adaptive control using only input-output measurements (DVS-MRAC-IO) for not strictly positive real systems with a relative degree of two is proposed. In order to show the effectiveness of the proposed controller, a detailed stability analysis is studied using Lyapunov theory. Further, a straightforward generalization of DVS-MRAC-IO for systems with arbitrary relative degree is presented. Numerical results are used to show the effectiveness of the proposed methods.

Motivated by the recent advance in adaptive output feedback control of affine nonlinear systems [8-10], an adaptive variable structure controller is proposed in this paper for solving the model reference adaptive control of nonlinear time-varying systems. Asymptotic output tracking performance can be achieved for relative degree one case. When the relative degree of the nonlinear system is greater than one, a systematic design procedure is given under a modified sector-type condition so that the closed-loop stability and the tracking performance are achieved similar to that in relative degree one case.

This article presents a global adaptive asymptotic tracking control method, capable of guaranteeing prescribed transient behavior for uncertain strict-feedback nonlinear systems with arbitrary relative degree and unknown control directions. Unlike most existing funnel controls that are built upon time-varying feedback gains, the proposed method is derived from a tracking error-dependent normalized function and a barrier function, together with a time-varying scaling transformation, leading to an improved prescribed performance control solution with the following features: 1) the developed control is embedded with normalized error based adaptive parameter tuning and is able to ensure asymptotic tracking; 2) given transient performance is guaranteed in that the tracking error preserves in the prescribed boundary for <inline-formula><tex-math notation="LaTeX">$\forall t\geq 0$</tex-math></inline-formula>; and 3) it is able to cope with nonlinear systems with arbitrary relative degree, mismatched uncertainties, and unknown control directions. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.

The double Y shift 30° PMSM two-motor series-connected system is supplied by one single inverter, which PMSM1 operates on dq plane and PMSM2 operates on zizi plane. To overcome the poor robustness and improve static and dynamic performance of adaptive back-stepping control approach suitable for the two-motor series-connected system is researched. And the adaptive back-stepping controller of PMSM1 is deduced on dq plane. The simulations compared with back-stepping controller show that adaptive back-stepping can improve the dynamic and static performances.

Compared with field oriented control (FOC), direct thrust control (DTC) is known to provide fast and robust response for permanent magnet linear synchronous motor (PMLSM). However, classical DTC produces notable thrust ripples because parameters variation and load perturbation. A novel adaptive variable structure controller is presented. The mover flux and thrust are controlled directly by adaptive variable structure controller, and mover voltage vectors calculated by the adaptive variable structure controller are applied to the motor by means of space vector modulation. Simulation results are presented to illustrate performances of the proposed method. The system provides smooth, fast mover speed and thrust responses and is robust with respect to motor parameters variation and load perturbations.

This paper presents an embedded adaptive robust controller for trajectory tracking and stabilization of an omnidirectional mobile platform with parameter variations and uncertainties caused by friction and slip. Based on a dynamic model of the platform, the adaptive controller to achieve point stabilization, trajectory tracking, and path following is synthesized via the adaptive backstepping approach. This robust adaptive controller is then implemented into a high-performance field-programmable gate array chip using hardware/software codesign technique and system-on-a-programmable-chip design concept with a reusable user intellectual property core library. Furthermore, a soft-core processor and a real-time operating system are embedded into the same chip for realizing the control law to steer the mobile platform. Simulation results are conducted to show the effectiveness and merit of the proposed control method in comparison with a conventional proportional-integral feedback controller. The performance and applicability of the proposed embedded adaptive controller are exemplified by conducting several experiments on an autonomous omnidirectional mobile robot.

This paper gives a new formulation of the robust observers for the minimum phase dynamical systems with arbitrary relative degrees (with respect to the relation between disturbance-output) by applying the implicit observer techniques. For plants with relative degree one, the robust observer is constructed without any a priori on the disturbance. For plants with relative degree two, an identification of the integral of the disturbance is made by using the variable structure approach, the state vector is asymptotically expressed by the integrals of the input and output and the estimation of the integrals of the disturbance. For plants with relative degree higher than two, the observer formulation is stated as a conjecture. Numerical examples and simulation results are presented to show the effectiveness of the proposed algorithms.

Robust adaptive integral backstepping control for opto-electronic tracking system based on modified LuGre friction model

Adaptive tracking control for a class of switched uncertain nonlinear systems under a new state-dependent switching law

Robustness and Alleviation of Chattering by New Modified Update Laws and Sigmoid Function in Variable Structure Adaptive Control