Sliding mode predictive tracking control for uncertain Steer-by-Wire system

The Steer-by-Wire (SbW) system is probably the most significant innovation among drive-by-Wire technologies in the automotive industry. Without the mechanical link, the most challenging issue is to control the wheels to closely follow the driver’s command. To improve the robustness of the model predictive control (MPC) in the presence of modeling uncertainties and disturbances in the steering control processes, a sliding mode predictive tracking control (SMPC) strategy for a SbW system with uncertain dynamics is proposed. The simulation and experimental results demonstrate that the performance of the proposed SMPC tracking controller is superior to both SMC and MPC methods for the steering angle tracking task.     

基于非线性块反步控制的无人直升机航迹跟踪算法研究

针对小型无人直升机系统高度非线性、强耦合和易受内外部扰动干扰的特点,提出了一种非线性块反步控制与广义比例积分观测器相结合的控制策略。该方法采用广义比例积分观测器构建多阶观测回路对系统状态量、扰动量及扰动量的多阶导数进行估计,然后将扰动的估计值代入到直升机系统模型中,采用反步法回归递推得到直升机的跟踪飞行控制律。通过对阶跃信号和复杂“8”字形航迹的航迹跟踪仿真,结果表明：在多种内外部扰动影响下,所设计的控制律具有良好的动态响应和航迹跟踪性能以及抗干扰能力。相较于常规非线性扰动观测器,广义比例积分观测器对高阶和快速时变扰动具有更高的预估精度,可以达到更好的扰动抑制效果。     

On tracking control for affine nonlinear systems by sliding mode

The stability problem of output tracking of a bounded time-varying reference by decouplable affine nonlinear systems using sliding mode control is investigated. It is shown that when the error dynamics on the sliding surface is chosen to be linear time-invariant, closed loop stability of systems under the presented sliding mode control can be guaranteed only if the systems are minimum phase.     

Sliding mode control with disturbance observer for a class of nonlinear systems

This paper is concerned with the stabilization problem for a class of nonlinear systems with disturbance. The disturbance model is unknown and the first derivative of disturbance is bounded. Firstly, a general disturbance observer is proposed to estimate disturbance approximatively. Secondly, since the bound of the disturbance observer error is unknown, an adaptive sliding mode controller is designed to guarantee that the state of system asymptotically converges to zero and the unknown bound can be adjusted by an adaptive law. Finally, an example is given to illustrate the effectiveness of the proposed method.     

Robust nonlinear generalised predictive control for a class of uncertain nonlinear systems via an integral sliding mode approach

In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.     

MIMO非线性不确定系统二阶滑模控制

提出了一种基于有限状态机切换策略的多输入多输出二阶滑模控制算法。算法保证了传统滑模控制对参数变化和扰动不灵敏的特点,削弱了滑模控制的“抖动”现象。在上界未知的测量噪声和参数变化的情况下,算法通过滑模量及其微分的符号构成控制律,实现了系统的镇定。仿真结果表明算法在噪声环境下能保证系统的稳定性,对参数不确定具有较强的鲁棒性。算法结构简单,便于实现。     

基于非线性干扰观测器的下肢外骨骼上楼梯滑模控制

针对下肢外骨骼在轨迹跟踪时对内部参数扰动和外界干扰较为敏感的特性,设计一种基于非线性干扰观测器的下肢外骨骼机器人滑模控制策略。首先建立下肢外骨骼上楼梯的动力学模型,分析其动力学特性;其次设计非线性干扰观测器,对下肢系统的不确定性和外部干扰进行观测;在此基础上,为保证系统轨迹跟踪误差的收敛性和减弱抖振,设计了低通滤波的滑模控制器,根据李雅普诺夫稳定性理论证明了下肢系统的稳定性;最后通过仿真与实验验证,该控制策略能够有效克服多种因素引起的干扰,改善系统的控制性能,提高系统的稳定性。     

Sliding mode control of singular stochastic hybrid systems

This paper is concerned with the sliding mode control (SMC) of nonlinear singular stochastic systems with Markovian switching. An integral sliding surface function is designed, and the resulting sliding mode dynamics is a full-order Markovian jump singular stochastic system. By introducing some specified matrices, a new sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic stability of the sliding mode dynamics. Then, a SMC law is synthesized for reaching motion. Moreover, when there exists an external disturbance, the ?₂ disturbance attenuation performance is analyzed for the sliding mode dynamics. Some related sufficient conditions are also established.     

含有非匹配干扰和未知动态的非仿射系统滑模控制算法

针对含有非匹配干扰和未知动态的非仿射系统控制问题,提出了一种基于扩张状态观测器(ESO)的改进滑模控制(SMC)方案.本文首先利用扩张状态观测器,将原系统转变为一个包含干扰的二阶积分级联系统,使含有未知动态的非仿射系统控制器设计问题转化为二阶积分级联系统的控制器设计问题,从而使得控制器在设计过程中不需要对对象模型完全已...     

Sliding mode control for time-varying delayed systems based on a reduced-order observer

In this paper, a stabilisation problem for a class of nonlinear systems is considered, where both the nonlinear term and the nonlinear uncertainty are mismatched and subject to time-varying delay. Under the assumption that the delay is known, a reduced-order observer is designed using an appropriate transformation. A sliding surface is proposed in an augmented space formed by the system outputs and the estimated states. The sliding mode dynamics are derived using an equivalent control approach, and the Lyapunov-Razumikhin approach is exploited to analyse the stability of the sliding motion. Then, a sliding mode control law is developed such that the system can be driven to the sliding surface in finite time. A simulation example shows the effectiveness of the proposed approach.     

Sliding mode control design for uncertain time‐delay systems subjected to a class of nonlinear inputs

A sliding mode controller is developed for uncertain time‐delay systems with a class of nonlinear inputs. Two main results are derived in this paper. The first result is the presentation of a new delay‐dependent stability condition of uncertain time‐delay systems. In a comparison example, this stability condition is shown to be less conservative than the ones reported recently. The second result is to present a new sliding mode control for uncertain time‐delay systems subjected to a class of nonlinear inputs. The stability of time‐delay systems with unmatching condition in the sliding mode is also discussed. Two illustrative examples are included to demonstrate the superiority of the obtained results. Copyright © 2003 John Wiley & Sons, Ltd.     

Sliding mode adaptive control for a class of nonlinear time‐varying systems

In this work, the problem of designing a control scheme capable of controlling dynamical systems with unknown time‐varying parameters and disturbances is proposed. In contrast with other works, based on two techniques, ie, adaptive backstepping and sliding modes, an improved method that guarantees the output asymptotic tracking of a smooth reference signal, the stability of the closed‐loop system, and the identification errors' boundedness is developed. By means of sliding mode observers, the adaptation errors' required information is extracted and injected to adaptive laws. The behavior of the proposed control scheme is analyzed by the Lyapunov method. The performance of the proposed system is verified with an academic example.     

Global tracking sliding mode control for a class of nonlinear systems via variable gain observer

A novel output‐feedback sliding mode control strategy is proposed for a class of single‐input single‐output (SISO) uncertain time‐varying nonlinear systems for which a norm state estimator can be implemented. Such a class encompasses minimum‐phase systems with nonlinearities affinely norm bounded by unmeasured states with growth rate depending nonlinearly on the measured system output and on the internal states related with the zero‐dynamics. The sliding surface is generated by using the state of a high gain observer (HGO) whereas a peaking free control amplitude is obtained via a norm observer. In contrast to the existing semi‐global sliding mode control solutions available in the literature for the class of plants considered here, the proposed scheme is free of peaking and achieves global tracking with respect to a small residual set. The key idea is to design a time‐varying HGO gain implementable from measurable signals. Copyright © 2010 John Wiley & Sons, Ltd.     

Type-2 fuzzy sliding mode control without reaching phase for nonlinear system

A new sliding mode control (SMC) algorithm for the nth order nonlinear system suffering from parameters uncertainty and subjected to an external perturbation is proposed. The algorithm employs a time-varying switching plane. At the initial time t=t₀, the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the plane moves to the origin of the state space. Since the nonlinear system is sensible to the perturbations and uncertainties during the reaching phase, the elimination of such phase yields in a considerable amelioration of system robustness. Switching plane is chosen such that: (1) the reaching phase is eliminated, (2) the nonlinear system is insensitive to the external disturbance and the model uncertainty from the initial time (3) the convergence of the tracking error to zero. Furthermore, a Type-2 fuzzy system is used to approximate system dynamics (assumed to be unknown) and to construct the equivalent controller such that: (1) all signals of closed-loop system are uniformly ultimately bounded, (2) the problems related to adaptive fuzzy controllers like singularity and constraints on the control gain are resolved. To ensure the robustness of the overall closed-loop system, analytical demonstration using Lyapunov theorem is considered. Finally, a robot manipulator is considered as a real time system in order to confirm the efficiency of the proposed approach. The experimentation is done for both regulation and tracking control problems.     

Robust adaptive backstepping control for a class of uncertain nonlinear systems based on disturbance observers

In this paper, a novel robust adaptive control scheme for a class of uncertain nonlinear systems is proposed using disturbance observer and backstepping method.Firstly, a disturbance observer is developed using radial basis function(RBF) neural network.The parameter updated law of the RBF neural network is given for monitoring subsystem disturbance well.The robust adaptive control scheme is then presented with backstepping method based on the designed disturbance observer.Semiglobal uniform ultimate bounded...     

Performance analysis of 2‐DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbances

In this paper, the tracking control problem is considered for a class of uncertain nonlinear systems with infinite discontinuous points in the external disturbance. The extended state observer–based 2‐degree‐of‐freedom control is used with one degree to estimate and cancel the “total disturbance” and the other to force the closed‐loop system to have desired characteristics. The tracking error between the state vector and its ideal trajectory in the entire transient process is adequately discussed to illuminate the performance of resulting control systems. The quantitative analysis shows that the tracking error can be small enough by tuning the bandwidth of the extended state observer. Moreover, the necessary and sufficient condition for the tracking error and the estimation error of the “total disturbance” to converge to zero is presented. The simulation results of a motion test demonstrate that the desired performance of the control system can be achieved despite discontinuous disturbance and nonlinear uncertainties.     

A geometric approach to multivariable control system design of a distillation column

A multivariable control problem of a distillation column is considered, where the object is to maintain two output variables, the compositions of the distillate and the bottom product at some desired values by manipulating the reflux flow rate and the boil-up rate.Based on a linearized model, a geometric approach is applied to the design problem of disturbance rejection control. In other words, a feedback control strategy is desired which enables the complete rejection of the effect of disturbances on both output variables.In obtaining the feedback control, the problem of how many and what state variables are to be measured and fed back has been made clear. In this control strategy, only five state variables are fed back. Thus, only five columns of the feedback gain matrix have non-zero values. Furthermore, two out of these five columns are uniquely determined, and the other three columns can be assigned arbitrary values and used for pole assignment of the controlled system.For the disturbances in composition and flow rate of the feed stream, Δx_F and ΔL_F, the effect of the disturbance Δx_F is completely rejected by the feedback controller, but the effect of the disturbance ΔL_F can only be eliminated from the output Δx_D.A digital simulation of a distillation column composed of nine plates, a condenser and a reboiler was carried out to confirm these results and to show that the linearized model used in this paper is valid for fairly large step changes.     

Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer

In this paper,the adaptive fuzzy tracking control is proposed for a class of multi-input and multioutput(MIMO)nonlinear systems in the presence of system uncertainties,unknown non-symmetric input saturation and external disturbances.Fuzzy logic systems(FLS)are used to approximate the system uncertainty of MIMO nonlinear systems.Then,the compound disturbance containing the approximation error and the timevarying external disturbance that cannot be directly measured are estimated via a disturbance observer.By appropriately choosing the gain matrix,the disturbance observer can approximate the compound disturbance well and the estimate error converges to a compact set.This control strategy is further extended to develop adaptive fuzzy tracking control for MIMO nonlinear systems by coping with practical issues in engineering applications,in particular unknown non-symmetric input saturation and control singularity.Within this setting,the disturbance observer technique is combined with the FLS approximation technique to compensate for the efects of unknown input saturation and control singularity.Lyapunov approach based analysis shows that semi-global uniform boundedness of the closed-loop signals is guaranteed under the proposed tracking control techniques.Numerical simulation results are presented to illustrate the efectiveness of the proposed tracking control schemes.     

一类受扰时滞离散系统的滑模跟踪控制

针对一类已知外扰结构的时滞离散系统,提出基于滑模的跟踪控制策略.将切换函数看作系统的输出,把原系统的滑模到达问题转化为对理想系统模型的跟踪问题.基于内模原理,针对误差系统与干扰模型的共同系统设计状态反馈控制律,实现了干扰抑制.从而说明原系统的状态可以跟踪理想系统的状态,使切换函数渐近稳定,避免了抖振的发生,并获得原系统状态的渐近稳定性.最后,给出的仿真算例说明了设计方法的可行性.     

Sliding mode control of switched hybrid systems with stochastic perturbation

This paper is concerned with the sliding mode control (SMC) of a continuous-time switched stochastic system. A sufficient condition for the existence of reduced-order sliding mode dynamics is derived and an explicit parametrization of the desired sliding surface is also given. Then, a sliding mode controller is then synthesized for reaching motion. Moreover, the observer-based SMC problem is also investigated. Some sufficient conditions are established for the existence and the solvability of the desired observer and the observer-based sliding mode controller is synthesized. Finally, numerical examples are provided to illustrate the effectiveness of the proposed theory.