Robust distributed attitude synchronization of multiple three-DOF experimental helicopters

Multiple experimental three-degrees-of-freedom (three-DOF) helicopters that are equipped with active disturbance systems constitute an attractive platform to validate robust control strategies. In this paper, a distributed synchronization controller is developed for such a platform, where each helicopter is subjected to unknown model uncertainties and external disturbances, and the desired trajectories are generated online, communicated through a network and not accessible by all helicopters. The controller is composed of a continuous tracker and a continuous uncertainty and disturbance estimator (UDE). The tracker makes the nominal closed-loop system globally asymptotically stable, and the UDE output is used to reject total uncertainties. The conditions that ensure zero-error tracking for each helicopter are identified; for the case with nonzero error, explicit relationship inequalities between the involved design parameters and the ultimate bound of error are revealed. Experimental results of four cases demonstrate improved tracking and synchronization accuracy of using the UDE with small parameters.     

Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft

In this article, we study the output tracking control of a class of MIMO nonlinear non-minimum phase systems in the presence of input disturbances. In order to attenuate the effects of disturbances, the method of uncertainty and disturbance estimator (UDE) is extended to the controller design for non-minimum phase systems. Due to the fact that the accumulated disturbances is composed of internal states and external disturbances, a different stability analysis is given, and the overall closed-loop system is proved to be semi-globally stable. The proposed state-feedback controller not only forces system outputs to asymptotically track desired trajectories, but also drives the unstable internal dynamics to follow bounded and causal ideal internal dynamics (IID) solved via stable system centre (SSC) method. Simulation results demonstrate that the proposed controller achieves excellent tracking and disturbance rejection performance via the example of VTOL aircraft which has been the benchmark of nonlinear non-minimum phase systems.     

Simultaneous fault estimation and fault-tolerant tracking control for uncertain nonlinear discrete-time systems

This paper deals with simultaneous fault estimation and control for a class of nonlinear systems with parameter uncertainty, which is described by Takagi–Sugeno (T–S) fuzzy model with parameter uncertainties and unknown disturbance. In this paper, a fuzzy reference model is used to generate error dynamic for tracking control. By considering actuator fault as an auxiliary state vector, we construct an augmented error system and propose a fault estimator/controller to achieve simultaneous fault estimation and fault-tolerant tracking control. H_∞ approach is used in the design of estimator/controller to attenuate the effect of the unknown disturbance and parameter uncertainties. The design conditions are formulated into a set of linear matrix inequalities (LMIs), which can be efficiently solved. Finally, a pitch-axis nonlinear missile model is used to illustrate the effectiveness of the proposed method.     

Finite‐time geometric control for underactuated aerial manipulators with unknown disturbances

In this article, the finite‐time geometric control for underactuated aerial manipulators is investigated. The dynamics of the aerial manipulator with unknown disturbances is analyzed first. The dynamics of the system is decomposed into the locked subsystem and shape subsystem. The finite‐time controller for the aerial manipulator is then designed based on the analyzed dynamics. In the controller, the attitude tracking error of the aircraft base is expressed from the rotation matrix, which makes the controller continuous and almost globally stable on SO(3). A continuous adaptive term is added in the controller to compensate for the unknown disturbances. Finite‐time filters are designed to ensure the smoothness of the commands on each loop. The convergence of the entire controlled system is strictly proved using Lyapunov theory and the definition of finite‐time stability. The results show that the tracking error and the disturbance bound estimation error of the entire system are finite‐time bounded near origin. Finally, comparative simulation results are presented to show the performance of the proposed controller.     

Robust adaptive self-structuring fuzzy control design for nonaffine,nonlinear systems

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L ₂ tracking performance to stabilise the closed-loop system. This L ₂ tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.     

On mean‐square H∞ control for discrete‐time nonlinear stochastic systems with (x,u, v)‐dependent noises

In this paper, the H_∞ control problem is investigated for a general class of discrete‐time nonlinear stochastic systems with state‐, control‐, and disturbance‐dependent noises (also called (x, u, v)‐dependent noises). In the system under study, the system state, the control input, and the disturbance input are all coupled with white noises, and this gives rise to considerable difficulties in the stability and H_∞ performance analysis. By using the inequality techniques, a sufficient condition is established for the existence of the desired controller such that the closed‐loop system is mean‐square asymptotically stable and also satisfies H_∞ performance constraint for all nonzero exogenous disturbances under the zero‐initial condition. The completing square technique is used to design the H_∞ controller with hope to reduce the resulting conservatism, and a special algebraic identity is employed to deal with the cross‐terms induced by (x, u, v)‐dependent noises. Several corollaries with simplified conditions are presented to facilitate the controller design. The effectiveness of the developed methods is demonstrated by two numerical examples with one concerning the multiplier‐accelerator macroeconomic system.     

Combining state estimator and disturbance observer in discrete‐time sliding mode controller design

In response to a multiple input/multiple output discrete‐time linear system with mismatched disturbances, an algorithm capable of performing estimated system states and unknown disturbances is proposed first, and then followed with the design of the controller. Attributed to the fact that both system states and disturbances can be estimated simultaneously with our proposed method, the estimation error is constrained at less than O(T) as the disturbance between the two sampling points is insignificant. In addition, the estimated system states and disturbances are then to be used in the controller when implementing our algorithm in a non‐minimum phase system (with respect to the relation between the output and the disturbance). The tracking error is constrained in a small bounded region and the system stability is guaranteed. Finally, a numerical example is presented to demonstrate the applicability of the proposed control scheme. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Decentralised direct adaptive fuzzy control for a class of large-scale nonaffine nonlinear systems and application to AHS

A novel decentralised direct adaptive fuzzy controller design is presented for a class of large-scale nonaffine uncertain nonlinear systems in this article. By integrating a fuzzy logic system and H _∞ tracking technique, the designed controller is able to adaptively compensate for interconnections and disturbances with unknown bounds, but none of the control and adaptation laws contains a sign function so that control chattering can be shunned. The closed-loop large-scale system is guaranteed to be asymptotically stable and obtain good H _∞ tracking performance. The control approach developed is applied to the following control problem of a string of vehicles within an automated highway system (AHS) and simulation results verify its validity.     

Sliding‐mode control of a three‐degrees‐of‐freedom nanopositioner

This paper presents the sliding‐mode control of a three‐degrees‐of‐freedom nanopositioner (Z, θ_x, θ_y). This nanopositioner is actuated by piezoelectric actuators. Capacitive gap sensors are used for position feedback. In order to design the feedback controller, the open‐loop characteristics of this nanopositioner are investigated. Based on the results of the investigation, each pair of piezoelectric actuators and corresponding gap sensors is treated as an independent system and modeled as a first‐order linear model coupled with hysteresis. When the model is identified and the hysteresis nonlinearity is linearized, a linear system model with uncertainty is used to design the controller. When designing the controller, the sliding‐mode disturbance (uncertainty) estimation and compensation scheme is used. The structure of the proposed controller is similar to that of a proportional integral derivative controller. Thus, it can be easily implemented. Experimental results show that 3‐nm tracking resolution can be obtained. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Backstepping Robust H ∞ Control for a Class of Uncertain Switched Nonlinear Systems Under Arbitrary Switchings

This paper addresses global robust H _∞ control for a class of switched nonlinear systems with uncertainty under arbitrary switchings. Each subsystem is in lower triangular form. The uncertainties are assumed to be in a known compact set. The backstepping design technique is used to design a smooth state feedback controller that renders the associated closed‐loop switched system globally robustly asymptotically stable and imposes a pre‐specified upper bound to the L ₂‐gain under arbitrary switchings. An example is provided to demonstrate the efficacy of the design approach.     

Resilient H∞ Control Design for Discrete‐Time Uncertain Linear Systems: An Auxiliary System Transformation Approach

This paper studies the resilient (non‐fragile) H∞ output‐feedback control design for discrete‐time uncertain linear systems with controller uncertainty. The design considers parametric norm‐bounded uncertainty in all state‐space matrices of the system, output and controller equations. The paper shows that the resilient H∞ output‐feedback control problem is equivalent to a scaled H∞ output‐feedback control problem of an auxiliary system without any system or controller uncertainty. Using the existing optimal H∞ design to solve the auxiliary system, the design guarantees that the resultant closed‐loop systems are quadratically stable with disturbance attenuation γ for all admissible system and controller uncertainties. A numerical example is given to illustrate the design method and its benefits.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Disturbance observer-based tracking control with prescribed performance specifications for a class of nonlinear systems subject to mismatched disturbances

This work investigates simultaneous prescribed performance tracking control and mismatched disturbance rejection problems for a class of strict-feedback nonlinear systems. A novel control scheme combining prescribed performance control, disturbance observer technique, and backstepping method is proposed. The disturbance estimations are introduced into the design of virtual control law design in each step to compensate the mismatched disturbances. To further improve the control performance, a prescribed performance function characterizing the error convergence rate, maximum overshoot, and steady-state error is used to construct the composite controller. The proposed controller guarantees transient and steady-state performance specifications of tracking error and provides much better disturbance attenuation ability simultaneously. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that all the states in the resulting closed-loop system are stable, and the tracking error evolves within the prescribed performance boundaries and asymptotically converges to zero even in the presence of mismatched external disturbances. Finally, theoretical results are illustrated and demonstrated by two simulation examples.     

Inertia‐free saturated output feedback attitude stabilization for uncertain spacecraft

In this article, the problem of robust output feedback attitude stabilization control for a class of uncertain spacecraft is investigated, which contains external disturbances, model parameter uncertainty, unknown and uncertain inertia, controller's gain perturbations, measurement errors, and input saturation. The aim of this work is to design a dynamic output feedback controller such that the closed‐loop attitude system is stabilized, while the H_∞ norm of the transfer function from the lumped disturbance and measurement error to output is ensured to be less than a pre‐specified disturbance attenuation level, and the actual control input is confined into a certain range simultaneously. Based on the Lyapunov theory, the existence conditions of such controller are derived in terms of linear matrix inequalities. It is worth mentioning that the controller's additive and multiplicative perturbations are accounted for respectively. An illustrative example is given to demonstrate the effectiveness and advantage of the proposed control design method.     

基于节能考虑的全向移动机器人鲁棒补偿轨迹跟踪控制

针对全向移动机器人在跟踪目标的过程中存在跟踪误差以及产生能量损耗的问题,首先构建一种新型机器人能耗模型,该模型能够有效预测机器人运行过程中各种能量消耗;其次,基于该能耗模型设置兼顾轨迹跟踪误差和能耗最小的性能指标函数,在其约束下,提出一种基于干扰鲁棒补偿的反馈节能控制器;然后,引入不确定性及干扰估计观测法,构建鲁棒补偿项,在满足能耗最优的前提下实现对外界干扰的有效抑制;最后,基于Lyapunov稳定性理论证明所提出的节能干扰鲁棒补偿控制系统是渐近稳定的.通过将所提出的控制器与比例微分控制器、$H_\infty$控制以及节能补偿控制进行比较,仿真结果表明,所提出的控制方法其控制精度更高、能量损耗更低、具有更强的鲁棒性.     

Robust control of uncertain nonlinear systems with state delays based on an uncertainty and disturbance estimator

In this article, one linear and one nonlinear robust control strategies are proposed for uncertain nonlinear continuous‐time systems with disturbances and state delays. The approaches are based on the uncertainty and disturbance estimator (UDE) introduced in 2004. In the case of a linear controller, the terms containing the nonlinear functions and time delays are treated as additional disturbances to the system. In the case of a nonlinear controller, both known and unknown delay scenarios are considered. In the case of an unknown time delay, the terms containing the delay are treated as additional disturbances to the system. The algorithms provide excellent tracking and disturbance rejection performance. Simulations are given to show the effectiveness of the strategies, first via a simple example and second via an application to a continuous stirred tank reactor system. Copyright © 2010 John Wiley & Sons, Ltd.     

Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator

This paper is concerned with the design of an asymptotically stabilizing tracking controller for an undamped wave equation modeling a piezoelectric stack actuator. For this, flatness‐based methods for trajectory planning and feedforward control are combined with dynamic feedback control involving a Luenberger‐type observer within the two degrees‐of‐freedom control concept. The asymptotic stability of the closed‐loop system is verified using Lyapunov's stability theory and LaSalle's invariance principle. Thereby, a separation theorem is introduced for bounded perturbations of infinitesimal generators of asymptotically stable C₀‐semigroups. Finally, the tracking performance is illustrated in simulation scenarios. Copyright © 2010 John Wiley & Sons, Ltd.     

Decoupling two-degree-of-freedom control strategy for cascade control systems

In this paper, two new two-degree-of-freedom control structures are proposed for cascade control systems, both of which are identical in the controller design procedure. The primary controller used for setpoint tracking is derived in terms of H₂ optimal performance objective. The secondary controller is responsible for rejecting load disturbances that seep into the intermediate process and therefore is called a load disturbance estimator, which is inversely figured out by proposing the desired complementary sensitivity function of the inner loop for disturbance rejection. As a result, the nominal setpoint response is decoupled with the load disturbance response of the inner loop, both of which can be optimized independently. Based on the control system stability analysis, the rule of thumb for tuning the single adjustable parameter of each controller is provided to cope with the process uncertainty in practice. Several illustrative examples are included to demonstrate the superiority of the proposed method.     

Robust H∞ control of uncertain singular systems based on equivalent‐input‐disturbance approach

In this paper, a robust H_∞ control problem is considered for an uncertain singular system. An active disturbance rejection method called equivalent input disturbance (EID) is used to reduce the influence of exogenous disturbances and uncertainties on the system. At the first, there exists an EID, which can produces the same effect on the system as disturbances and uncertainties do in the control channel according to the EID concept. Then, an EID estimator is constructed to estimate the influence of EID on the system. Finally, based on Lyapunov stability theory, a static output feedback‐based robust H_∞ controller combined with EID estimate is designed, guaranteeing that closed‐loop system is admissible (regular, impulse‐free, and stable) with a prescribed H_∞ performance level. Compared with traditional H_∞ control method, H_∞ control based on EID method improve the control performance of the system. A numerical example demonstrates the validity of the method.     

Distributed adaptive robust tracking and model matching control with actuator faults and interconnection failures

In this paper, direct adaptive-state feedback control schemes are developed to solve the robust tracking and model matching control problem for a class of distributed large scale systems with actuator faults, faulty and perturbed interconnection links, and external disturbances. The adaptation laws are proposed to update the controller parameters on-line when all the eventual faults, the upper bounds of perturbations and disturbances are assumed to be unknown. Then a class of distributed state feedback controllers is constructed to automatically compensate the fault, perturbation and disturbance effects based on the information from adaptive schemes. The proposed distributed adaptive tracking controller can ensure that the resulting adaptive closed-loop large-scale system is stable and the tracking error decreases asymptotically to zero in the presence of uncertain faults of actuators and interconnections, perturbations in interconnection channels, and disturbances. The proposed adaptive design technique is finally evaluated in the light of a simulation example.