Task-level approaches for the control of constrained multibody systems

This paper presents a task-level control methodology for the general class of holonomically constrained multibody systems. As a point of departure, the general formulation of constrained dynamical systems is reviewed with respect to multiplier and minimization approaches. Subsequently, the operational space framework is considered and the underlying symmetry between constrained dynamics and operational space control is discussed. Motivated by this symmetry, approaches for constrained task-level control are presented which cast the general formulation of constrained multibody systems into a task space setting using the operational space framework. This provides a means of exploiting task-level control structures, native to operational space control, within the context of constrained systems. This allows us to naturally synthesize dynamic compensation for a multibody system, that properly accounts for the system constraints while performing a control task. A set of examples illustrate this control implementation. Additionally, the inclusion of flexible bodies in this approach is addressed.     

An optimal feedforward control design for the set-point following of MIMO processes

In this paper we propose a new methodology for the design of a feedforward action for the improvement of the set-point following performance of feedback controlled square MIMO processes. In particular, by exploiting an analytical decoupling technique, the feedforward signals are determined in order to achieve predefined output transition times, by assuming that the transfer function matrix of the system consists of first order plus dead time transfer functions. An analytical expression of the feedforward signal is derived and this allows to solve easily a multiobjective optimisation problem in order to minimise the transition time of each output subject to constraints of the actuators. Simulation as well as experimental results demonstrate the effectiveness of the method.     

Inversion-based feedforward and reference signal design for fractional constrained control systems

In this paper we propose a solution for the synthesis of a feedforward control action for a fractional control system. In particular, an input–output inversion based methodology is devised in order to determine the open-loop signal that provides a predefined process variable transition from a steady-state value to another. The transition time is then minimized subject to constraints on the process and control variables and their derivatives. Simulation results show the effectiveness of the technique.     

A robust adaptive feedforward control in repetitive control design for linear systems

This paper proposes a new adaptive feedforward cancellation (AFC) control that achieves periodic tracking and/or periodic disturbance rejection. The new control design is a direct scheme in the sense that it adaptively updates the desired control without estimating the unknown disturbance. The proposed new control has several advantages. First, its adaptation gain can be arbitrarily chosen without upsetting the system stability if given the exact system model. Second, it can be applied to not only minimum-phase systems, but also non-minimum phase systems. Third, the new control law is independent of where the disturbance enters the system. Finally, a robustness analysis is made to show that the proposed control is robust with respect to un-modelled dynamics.     

A new approach to inversion-based feedforward control design for nonlinear systems

The finite-time transition between stationary setpoints of nonlinear SISO systems is considered as a scenario for the presentation of a new design approach for inversion-based feedforward control. Design techniques which are based on a stable system inversion result in input trajectories with pre- and/or post-actuation intervals. The presented approach treats the considered transition task as a two-point boundary value problem (BVP) and yields causal feedforward trajectories, which are constant outside the transition interval. The main idea of this approach is to provide free parameters in the desired output trajectory to solve the BVP of the internal dynamics. Thereby, a standard MATLAB function can be used for the numerical solution of the BVP. Feedforward control design techniques are illustrated by simulation results for a simple example.     

Inverse optimal control for strict‐feedforward nonlinear systems with input delays

We consider inverse optimal control for strict‐feedforward systems with input delays. A basic predictor control is designed for compensation for this class of nonlinear systems. Furthermore, the proposed predictor control is inverse optimal with respect to a meaningful differential game problem. For a class of linearizable strict‐feedforward system, an explicit formula for compensation for input delay, which is also inverse optimal with respect to a meaningful differential game problem, is also acquired. A cart with an inverted pendulum system is given to illustrate the validity of the proposed method.     

网络化控制系统中鲁棒控制器的设计与优化

针对网络化控制系统,提出了新型的延迟状态变量模型,考虑到模型的不确定因素和外 部扰动,推出了鲁棒控制器存在的条件,并给出了该控制器设计和性能优化的方法。仿真结果表明, 该控制器对所有允许的网络延迟、模型不确定性和外部扰动,具有良好的性能。     

Wiener-Hopf design of servo-regulator-type multivariable control systems including feedforward compensation

Frequency-domain design in a quadratic cost setting is treated for a multivariable control system which includes disturbance feedforward, output feedback, and reference-input compensation (i.e. a three-degrees-of-freedom control system). The cost function is taken to account for tracking accuracy, plant saturation and plant sensitivity. The class of all controllers is determined for which the given system is internally asymptotically stable and the quadratic cost function is finite. This controller class is parametrized in terms of arbitrary real rational matrices Z_z Z_u and Z_w which are strictly proper and analytic in Re s ≥ 0. The optimal solution is obtained by setting the Z matrices to zero.     

Inversion-based feedforward control design for linear transport systems with spatially acting input

The considered transport systems, which possess an actuator with a spatial influence characteristic along the transport path, are used for the transport of material between different process stages and for the conditioning of the conveyed goods at the same time. The spatially acting input results in complex input/output behaviour of a Single-Input Single-Output (SISO) system with distributed delays. The feedforward control task under consideration is defined by a setpoint change of the subsequent process stage. For the feedforward controller design, an inversion-based approach in the frequency domain is investigated to steer the output of the transport system towards a predefined constant value. In order to compensate model uncertainties and reject unknown disturbances, the results of the inversion-based feedforward control are used to design a feedback controller.     

网络化切换控制系统故障检测与优化设计

研究存在未知短时延、丢包和系统不确定性的网络化切换控制系统故障检测与时域优化问题. 首先基 于观测器构建残差发生器, 结合Lyapunov 函数方法和平均驻留时间方法分析系统的稳定性, 并以线性矩阵不等式(LMI) 形式给出故障检测滤波器的求解方法; 然后为了改善故障检测系统的性能, 采用后置滤波器对残差信号进行时域优化, 并利用奇偶空间方法给出其最优解; 最后设计并推导出自适应阈值. 仿真结果验证了所提出方法的有效性.

     

Sensitivity-based feedforward and feedback control for uncertain systems

In many control applications, we are interested in accurate trajectory tracking. This is especially true for cases in which exact analytic solutions are not available because initial states are not consistent with the desired state or output trajectories or because parameters are significantly uncertain. In these cases, control strategies can be derived on the basis of a verified sensitivity analysis. For that purpose, we have to define suitable performance indices which describe the deviation between the actual and desired trajectories. In this paper, an overview of different sensitivity-based control procedures is given. These procedures include tracking control for systems with bounded parameter uncertainties as well as measurement errors described by interval variables. Moreover, we present a first verified approach to automatic path following by means of an automatic modification of desired output trajectories. This procedure is necessary in cases in which exact trajectory tracking is not possible due to the violation of control constraints.     

Periodic motion planning and control for underactuated mechanical systems

We consider the problem of periodic motion planning and of designing stabilising feedback control laws for such motions in underactuated mechanical systems. A novel periodic motion planning method is proposed. Each state is parametrised by a truncated Fourier series. Then we use numerical optimisation to search for the parameters of the trigonometric polynomial exploiting the measure of discrepancy in satisfying the passive dynamics equations as a performance index. Thus an almost feasible periodic motion is found. Then a linear controller is designed and stability analysis is given to verify that solutions of the closed-loop system stay inside a tube around the planned approximately feasible periodic trajectory. Experimental results for a double rotary pendulum are shown, while numerical simulations are given for models of a spacecraft with liquid sloshing and of a chain of mass spring system.     

Pulse control of flexible multibody systems

An active pulse control method is developed to reduce the vibrations of multibody systems resulting from impact loadings. The pulse, which is a function of system generalized coordinates and velocities, is determined analytically using energy and momentum balance equations of the impacting bodies. Elastic components in the multibody system are discretized using the finite element method. The system equations of motions and nonlinear algebraic constraint equations describing mechanical joints between different components are written in the Lagrangian formulation using a finite set of coupled reference position and local elastic generalized coordinates. A set of independent differential equations are identified by the generalized coordinate partitioning of the constraint Jacobian matrix. These equations are written in the state space formulation and integrated forward in time using a direct numerical integration method. Dependent coordinates are then determined using the constraint kinematic relations. Points in time at which impact occurs are monitored by an impact predictor function, which controls the integration algorithms and forces for the solution of the momentum relation, to define the jump discontinuities in the composite velocity vector as well as the system reaction forces. The effectiveness of the active pulse control in reducing the vibration of flexible multibody aircraft during the touchdown impact is investigated and numerical results are presented.     

含不等式约束的欠驱动系统约束跟随控制

在运动控制领域, 欠驱动机械系统通常需要满足一系列的等式约束(完整或非完整的)以便获得较好的运动 表现, 同时出于安全考虑还需要满足一定的不等式约束条件. 本文提出了一种约束跟随控制方法, 用以解决同时含 等式和不等式约束的欠驱动系统控制问题. 该控制设计主要分为两步: 第1步: 只考虑系统需要满足的等式约束, 运 用约束跟随控制方法推导出基于系统模型的状态反馈控制律; 第2步: 考虑系统需要满足的不等式约束, 先通过状 态变量映射将不等式约束整合到原等式约束中以得到新的等式约束, 再基于新的等式约束和第1步所述的约束跟随 控制方法, 推导出系统所需的状态反馈控制律. 将该约束跟随控制方法应用于三自由度非线性强耦合的欠驱动平面 垂直起降(PVTOL)飞行器. 仿真结果表明, 该控制方法能有效处理PVTOL飞行器运动过程中需满足的等式约束(轨 迹跟踪和姿态保持)和不等式约束(边界服从).     

Hybrid control for a class of underactuated mechanical systems

This paper considers a stabilizing hybrid scheme to control a class of underactuated mechanical systems. The hybrid controller consists of a collection of state feedback controllers plus a discrete-event supervisor. When the continuous-state hits a switching boundary, a new controller is applied to the plant. Lyapunov theory is used to determine the switching boundaries and to guarantee the stability of the closed-loop hybrid system. This approach is applied to the well-known swing up and balancing control problem of the inverted pendulum     

垂直三连杆欠驱动机械臂通用控制策略设计

本文针对一类含单一欠驱动关节的垂直三连杆欠驱动机械臂提出一种基于振荡衰减轨迹的通用控制策略.与传统的分区控制策略相比,本文控制策略无需采用分区方式就能快速地实现将机械臂末端点由垂直向下初始位置开始移动,并最终稳定在垂直向上目标位置的控制目标.首先,根据驱动连杆的初始和目标状态,为驱动连杆规划含可调参数的振荡衰减轨迹.该轨迹能够在一定调节时间内将驱动连杆直接由初始状态移动至目标状态.基于连杆状态间的耦合关系,利用粒子群优化算法优化轨迹参数使欠驱动连杆在相同调节时间内也运动至目标状态.接着,利用滑模方法设计跟踪控制器使驱动连杆跟踪优化后的振荡衰减轨迹,这样,系统末端点将由初始位置移动至目标位置.进一步利用极点配置方法设计镇定控制器克服重力的作用将末端点稳定在目标位置.最后,通过仿真实验验证所提控制策略的有效性.     

Robust optimal design and convergence properties analysis of iterative learning control approaches

In this paper, we address four major issues in the field of iterative learning control (ILC) theory and design. The first issue is concerned with ILC design in the presence of system interval uncertainties. Targeting at time-optimal (fastest convergence) and robustness properties concurrently, we formulate the ILC design into a min-max optimization problem and provide a systematic solution for linear-type ILC consisting of the first-order and higher-order ILC schemes. Inherently relating to the first issue, the second issue is concerned with the performance evaluation of various ILC schemes. Convergence speed is one of the most important factors in ILC. A learning performance index—Q-factor—is introduced, which provides a rigorous and quantified evaluation criterion for comparing the convergence speed of various ILC schemes. We further explore a key issue: how does the system dynamics affect the learning performance. By associating the time weighted norm with the supreme norm, we disclose the dynamics impact in ILC, which can be assessed by global uniform bound and monotonicity in iteration domain. Finally we address a rather controversial issue in ILC: can the higher-order ILC outperform the lower-order ILC in terms of convergence speed and robustness? By applying the min-max design, which is robust and optimal, and conducting rigorous analysis, we reach the conclusion that the Q-factor of ILC sequences of lower-order ILC is lower than that of higher-order ILC in terms of the time-weighted norm.     

Neural networks for feedback feedforward nonlinear control systems

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.