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.     

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.     

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.     

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     

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.     

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.     

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.     

A hybrid switching control strategy for nonlinear and underactuated mechanical systems

This note presents a hybrid switching control strategy for nonlinear and underactuated mechanical systems. Sufficient conditions for constructing the hybrid switching control, stability proof, and experimental results for using the hybrid switching control are given.     

Passivity-based control of nonlinear flexible multibody systems

In this paper, global asymptotic stability of a class of nonlinear multibody flexible space structures under certain dissipative compensation is established. Furthermore, for an important subclass of such systems, the stability is shown to be robust to certain types of actuator and sensor nonlinearities. The results are applicable to robust stabilization of a wide class of systems, including flexible space structures and manipulators with articulated flexible appendages. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems     

Two algorithms for frequency domain design of robust control systems

Two algorithms are described that are useful in the computer-aided design implementation of the robust controller design scheme proposed by Horowitz (1963) and Horowitz and Sidi (1972).     

一类欠驱动系统的控制方法综述

近年来欠驱动系统已经成为机器人与自动控制领域的研究热点之一,本文对一类欠驱动系统(欠驱动连杆系统)的控制方法的研究状况进行了综述.首先给出了欠驱动系统的动力学模型,并介绍了2种基本控制模式;随后,对其主要的控制方法,包括最优控制方法、运动规划法、部分反馈线性化方法、能量(无源)方法、变量降维法、分级控制设计方法及智能控制方法,展开了分析与讨论;在此基础之上,对欠驱动连杆控制系统设计存在的抗干扰性、实用性及快速性等主要问题进行了简要分析,并就今后的研究方向进行了展望,如鲁棒策略、饱和控制与有限时间控制等.     

Global output feedback control for uncertain nonlinear feedforward systems

This paper considers a class of uncertain nonlinear feedforward systems with unknown constant growth rate, output polynomial function growth rate and system input function growth rate. Under the most general growth rate condition, only one dynamic gain is used to compensate simultaneously these three types of growth rates, an output feedback controller is constructed to guarantee the boundedness of closed-loop system states and the convergence of original system states.     

Dynamics and control of a class of underactuated mechanical systems

This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable