Direct adaptive compensation for actuator failures and dead-Zone constraints in tracking control of uncertain nonlinear systems

doi:10.1016/j.ins.2017.06.029

Information Sciences

Volume 417, November 2017, Pages 328-343

https://doi.org/10.1016/j.ins.2017.06.029 Get rights and content

Abstract

In this paper, a new tuning function backstepping control scheme is proposed for a class of parametric strict feedback nonlinear systems to accommodate actuator failures/faults and dead-zone constraints, where the failures/faults are uncertain in time, pattern, and values, and the dead-zone parameters are not available for feedback control design. Roughly speaking, such a scheme is developed in two steps below. First, by using an adaptive smooth inverse function to compensate for the dead-zone nonlinearity, we separate the coupling actuator dynamics into two parts, i.e., the dead-zone compensation errors and the nominal failure dynamics. Afterward, we further handle these two parts based on the techniques of robust adaptive approach and parametrization method. With our scheme, the global boundedness of the signals in the closed-loop system are ensured, and the tracking error is steered to zero asymptotically, regardless of the presence of uncertain failures/faults and dead-zone constraints. These results have also been verified through simulation studies.

Introduction

In a practical control system, actuator components may suffer from nonsmooth nonlinearities such as dead zone, saturation, backlash, hysteresis, etc. In most cases, these nonlinearities will impose damaging effects on the system performance, or even lead to instability of the closed-loop system. To compensate the hysteresis and backlash nonlinearities in some physical systems and devices, several adaptive control schemes have been proposed in [6], [7], [8], [9], [10], [11], [16], [21], [24], [25], [26], [27], [42], [47], [48], [55]. Apart from these, it is particularly important to point out that dead-zone characteristic ubiquitously exists in gear friction, hydraulic valves, DC motors and mechanical connection, which usually degrades the performance of the system. In recent years, adaptive compensation control schemes for dead-zone nonlinearity in the presence of parametric uncertainties have been developed. In [15], [22], [28], [31], [32], [40], [49], the dead-zone nonlinearity is regarded as an external bounded disturbance which can be mitigated through robust control design by using a direct decomposition method (DDM). Based on the DDM, in Zhang et al. [51], [52] and Li et al. [17], [18], several outstanding adaptive robust control schemes are further proposed to compensate generalized actuator dead-zones. Apart from DDM, the inverse compensation method (ICM) is another effective strategy to eliminate the effects of nonsmooth nonlinearities. Compared to the compensation method DDM, ICM can completely cancel actuator dead-zone by constructing an inverse compensator through parameter identification; see [31]. However, it is usually interminable and costly for offline parameter identification. Thus it is of significance to develop an adaptive inverse compensation method (AICM) by using the adaptive technique to estimate unknown dead-zone parameters online; see [38]. Furthermore, AICM is utilized to construct an advanced adaptive dead-zone inverse compensator in [39]. Moreover, in [54], a smooth adaptive dead-zone inverse for avoiding chattering phenomenon is proposed, and a different adaptive compensation scheme for unknown dead-zone is achieved in [14].

Besides the inherent actuator nonlinearities mentioned above, the failures/faults of suddenly getting stuck and losing partial effectiveness may also occur in practical actuation mechanisms, as pointed out in [33], [34], [35]. To handle such faults, the adaptive control methodology is mostly applied to the nonlinear system, see, e.g., [1], [2], [3], [5], [41], [43], [44], [45], [53]. Recently, studies on actuator failures started by handling the linear system failure in [36], [37], and the results were further extended to nonlinear system failure in [33], [34], [35] by the utilizing backstepping technique. With backstepping recursive design, a new prescribed performance bounds (PPB) based controller is proposed in [44] to guarantee the tracking error within the prescribed lower and upper bounds. Moreover, in the recent work [20], a robust adaptive fault-tolerant control scheme is further proposed for compensating failures in dead-zone actuators. However, such a scheme mainly treats the actuator failures and dead-zone nonlinearity as bounded disturbance-like effects, and thus the perfect asymptotic tracking performance cannot be obtained even for the case of finite number of actuator failures.

Motivated by observations above, in this paper, we study the problem of direct adaptive failure compensation control for a class of uncertain multiple inputs and single output (MISO) nonlinear systems with actuator failures and dead-zone constraints. The nonsmooth dead-zone nonlinearity and actuator failures are coupled in actuators, leading to a nontrivial task to construct the desirable capable of ensuring stability in the sense of global boundedness, and perfect asymptotic output tracking. Such a challenge is successfully addressed with our newly proposed control methodology with the following contributions.

1.
Note that we take actuator failures and dead-zone nonlinearities into account simultaneously in control design, which thus is more general than the existing works [13], [17], [18], [28], [31], [40], [46], [49], [54] that only considered dead-zone effect and [1], [2], [3], [19], [33], [34], [35], [41], [44], [45] that solely focused on actuator failure compensation. Moreover, perfect asymptotic tracking control performance is achieved with our scheme, irrespective of the existence of such both adversaries.
2.
The smooth adaptive inverse is firstly utilized to compensate for actuator dead-zone nonlinearity, such that the compensating errors containing failure parameters between actual function value of dead-zone nonlinearity and its designed dead-zone output, which is then eliminated in the subsequent control design.
3.
Recently, the authors in [20] proposed a new and novel robust adaptive control scheme, which has been shown to be applicable to compensate for actuator dead-zone and failures/faults. However, such a scheme cannot recover the perfect asymptotic tracking performance when the number of actuator failures become finite. This issue is also successfully addressed with our proposed scheme.

The outline of the paper is organized below. In Section 2, the control problem is formulated, and the related assumptions are given. In Section 3, based on backstepping recursive design, a desired controller for addressing control problems is constructed and the stability analysis is provided at the end of this section. Simulations on nonlinear system with dead-zone and failures/faults are shown in Section 4. Finally, we conclude the paper in Section 5.

Section snippets

System model and problem statement

In this paper, the following uncertain nonlinear system for the adaptive actuator failure compensation problem is considered. $\dot{x} = f_{0} + \sum_{i = 1}^{p} ϑ_{i} f_{i} (x) + \sum_{j = 1}^{q} b_{j} g_{j} (x) u_{j}$ $y = h (x)$ where x ∈ ℜⁿ are state variables, y ∈ ℜ is the system output, u_j ∈ ℜ for $j = 1, 2, \dots, q$ denotes the jth control input to the plant, f_i(x) ∈ ℜⁿ for $i = 0, 1, \dots, p, g_{j} (x) \in ℜ^{n}$ for $j = 1, 2, \dots, q$ and h(x) are known smooth nonlinear functions, and ϑ_i for $i = 1, 2, \dots, p$ and b_j for $j = 1, 2, \dots, q$ are unknown parameters and control coefficients, respectively.

Denote τ_j

Dead-zone inverse model

In this part, to prevent the system from potential chattering phenomenon in the backstepping recursion, the following smooth dead-zone inverse model is employed for the control design: $τ_{j} = \frac{v_{j} + m_{r} d_{+}}{m_{r}} Φ_{1} (v_{j}) + \frac{v_{j} + m_{l} d_{-}}{m_{l}} Φ_{2} (v_{j})$ where $j = 1, 2, \dots, q,$ Φ₁(v_j) and Φ₂(v_j) are designed as smooth continuous functions as: $Φ_{1} (v_{j}) = \frac{e^{\frac{v_{j}}{e_{0}}}}{e^{\frac{- v_{j}}{e_{0}}} + e^{\frac{v_{j}}{e_{0}}}}, Φ_{2} (v_{j}) = \frac{e^{- \frac{v_{j}}{e_{0}}}}{e^{\frac{- v_{j}}{e_{0}}} + e^{\frac{v_{j}}{e_{0}}}}$ where e₀ > 0 is a user-defined parameter.

For illustration, model (4) can be expressed in another form: $v_{j} = - θ_{j}^{T} w_{j}$ for $j = 1, 2, \dots, q,$ where $θ_{j}^{T} = [m_{r}, m_{r} d_{+}, m_{l}$

Simulation studies

In this section, the numerical examples are considered to illustrate the previous methodology for compensating the dead-zone actuators with unknown failures.

Conclusion

In this paper, we consider the problem of adaptive tracking control for parametric-strict-feedback system with dead-zone actuators and possible failures/faults. To resolve such a problem, a novel adaptive controller for accommodating is presented based on the backstepping scheme. In our controller design, a smooth adaptive inverse model of dead-zone is utilized to compensate for the effects of dead-zone nonlinearity and then the compensating errors with failure parameters are obtained.

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^☆: This work was supported in part by the National Natural Science Foundation of China under Grant 61573108, in part by National Natural Science Foundation of China (U1501251), in part by the Natural Science Foundation of Guangdong Province 2016A030313715, in part by the Natural Science Foundation of Guangdong Province through the Science Fund for Distinguished Young Scholars under Grant S20120011437, in part by the Ministry of Education of New Century Excellent Talent under Grant NCET-12-0637.

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Direct adaptive compensation for actuator failures and dead-Zone constraints in tracking control of uncertain nonlinear systems☆

Abstract

Introduction

Section snippets

System model and problem statement

Dead-zone inverse model

Simulation studies

Conclusion

Automatica

Appl. Math. Comput.

IEEE Trans. Syst. Man, Cybern.

Inf. Sci.

IEEE Trans. Cybern.

Automatica

ISA Trans.

J. Math. Anal. Appl.

Inf. Sci.

Automatica

Automatica

J. Franklin Inst.

Inf. Sci.

Automatica

Automatica

Automatica

Automatica

Inf. Sci.

Multivariable adaptive algorithms for reconfigurable flight control

IEEE Trans. Control Syst. Technol.

Multiple-model adaptive flight control scheme for accommodation of actuator failures

J. Guidance, Control, Dyn.

Robust adaptive failure compensation of hysteretic actuators for parametric strict feedback systems

2011 50th IEEE Conference on Decision and Control and European Control Conference

Adaptive inverse control for parametric strict feedback systems with unknown failures of hysteretic actuators

Int. J. Robust Nonlinear Control

Positive solutions to boundary value problems of p -Laplacian with fractional derivative

Boundary Value Prob.

Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model

J. Inequalities Appl.

High performance adaptive robust control for nonlinear system with unknown input backlash

Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009

Adaptive control approach for improving control systems with unknown backlash

2011 11th International Conference on Control, Automation and Systems (ICCAS)

Robust control of systems involving non-smooth nonlinearities using modified sliding manifolds

American Control Conference, 1998. Proceedings of the 1998