Modal analysis and control of a rotating Euler-Bernoulli beam part II: Residual vibration control

The crucial control system characteristics and analysis for distributed parameter system is illustrated and a new control scheme is presented by application to feedback control of a Euler-Bernoulli beam. The present paper is a continuation of [1] and a input preshaping technique based on frequency domain analysis is applied for the flexible link. For the application areas of a flexible link, the overshoot may not be welcome in spray painting, arc welding, and assembly of mechanical parts. This shaped input technique together with the designed controller can yield the shortest actual system input that makes the corresponding closed-loop system of the flexible link time-optimal operation, high accuracy, and energy efficiency.     

An entire strategy for precise system tracking control of a revolving thin flexural link,part I: Finite element modeling and direct tuning controller design

An entire control strategy including a design based model, controller design, and system output modification for a distributed parameter system is illuminated by application to feedback control of a revolving thin flexural link. In Part I, a very realizable actuator and a sensor, which uses a motor and a tachometer, are applied to design the control system. The finite element modeling and the state space representation are obtained for the purpose of control system analysis and computer simulation. Instead of relying on parameter identification subroutines, a controller design based on directly tuning the parameter of the gain makes the closed-loop absolutely stable and good for system tracking control. This control system design scheme is robust, insensitive to system parameter changes, and this algorithm cannot depend on traditionally priori knowledge such as the system dimension, exact model, or observer design. The performance included in the presence of all the high frequency dynamics can be effectively shown through the computer simulation, and one is led to speculate that this design scheme may perform quite well in the real world implementation.     

Identification and Self Tuning Control for Active Magnetic Bearing Systems: Levitation of Unknown Rotors

The present paper deals with the problem of levitating rotors with unknown characteristics by means of active magnetic bearings whose properties are known. This problem is of interest in a technical setting to shorten the development time of AMB systems, in particular for controller design. Theoretical interest arises from the fact that several issues in the area of identification and self tuning control are addressed for an unstable system. Our aim is to identify the flexible rotor including gyroscopic effects and to automatically design a robustly stabilizing controller for this system that can be used for running the system under regular operating conditions. To this end, a rigid body model of the rotor is identified based on measured step responses from the plant. Then, the bearings are adjusted to have very low stiffness, and a controller with steep roll‐off is designed in order to avoid excitation of the unknown flexible modes of the system. Once the rotor is floating, the identification algorithm from [1] is applied to obtain information on the flexible modes of the system. Based on this extended model, a robust controller allowing for slow rotation of the rotor is designed. With the rotor rotating at a moderate speed, the frequency response functions are measured, and based on these measurements, the gyroscopic matrixof the system is identified, completing the system model and allowing for design of the desired controller for normal operation. The present contribution focusses on identification of the rigid body model of the flexible rotor.     

The galerkin method and feedback control of linear distributed parameter systems

In the development of feedback control theory for distributed parameter systems (DPS), i.e., systems described by partial differential equations, it is important to maintain the finite dimensionality of the controller even though the DPS is infinite dimensional. Since this dimension is directly related to the available on-line computer capacity, it must be finite (and not very large) in order to make the controller implementable from an engineering standpoint. In previous work, it has been our intention to investigate what can be accomplished by finite-dimensional control of infinite-dimensional systems; in particular, we have concentrated on controller design and closed-loop stability. The starting point for all of this is some means for producing a finite-dimensional approximation—a reduced-order model—of the actual DPS. When the “modes” of the DPS are known, the natural candidate for model reduction is projection onto the modal subspace spanned by a finite number of critical modes. Unfortunately, in real engineering systems, these modes are never known exactly and some other reasonable approximation must be used. In this paper, the model reduction is based on the well-known Galerkin procedure. We generate the Galerkin reduced-order model and develop a finite-dimensional controller from it; then we analyze the stability of this controller in closed loop with the actual DPS. Our results indicate conditions under which model reduction based on consistent Galerkin approximations will lead to stable finite-dimensional control.     

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part I: A unified approach to the design of Llnear control system

Due to difficulties in modeling and poor knowledge of parameters, the behavior of flexible structures is subject to significant uncertainty. Hence it is essential that the control system provide an absolutely stable property in the presence of large variations. Over the years, many control laws—proportion and derivative (PD) control, nonlinear, linear-quadratic, adaptive, and linear quadratic Gaussian (LQG)—have been synthesized for flexible structures. The most commonly applied are the LQG controllers. In spite of its attractive qualities, the LQG controller is sensitive to parameter variations, and therefore its performance will deteriorate when the payload or typical parameters of the system vary with time. At the same time, the LQG controller does not guarantee general stability margins, and this is, perhaps, its main drawback. On the other hand, the PD is one kind of controller that ensures system stability to parameter variations within a certain bound. But a problem with the PD controller is evident; when high-frequency noise is present in the system, this noise will be amplified by the PD controller, which is generally unacceptable. In this paper, instead of using a PD controller, a passive lead compensator is employed, so that

• 1.(1) no additional power supplies are required and
• 2.(2) noise due to differentiation is reduced.

This lead compensator, together with a composite control strategy designed by the most popularly used sensors, potentiometer and tachometer, for the corresponding closed-loop system, has been shown with very good agreement in terms of system performance requirement. For the design of control system, it is practical to first design the controller based on the linear system model by neglecting the nonlinearities of the system. In Part I, the lead compensator, together with complementary control strategy and computer simulation modeling for a rotating flexible structure, with particular application to elastic rod system, is presented for the linear control system. Then the designed controller is applied to the nonlinear system model for evaluation and redesigned by computer simulation. This will be presented in Part II.     

Unwanted noise and vibration control using finite element analysis and artificial intelligence

A mechatronic approach integrating both passive and active controllers is presented in this study to deal with unwanted noise and vibration produced in an automobile wiper system operation. Wiper system is a flexible structure with high order, nonlinear model that is considered as a multi objective control problem since there is a conflict between its functionality quality in wiping and generated unwanted noise and vibration. A passive control technique using multi body system (MBS) model and finite element analysis (FEA) is introduced to identify the potential of the effectiveness of the physical parameters of wiper blade to give appropriate range to reduce the unwanted noise and vibration in the system. While, the significant contribution of active controller is to deal with uncertainties exerted to system within wiper operation. In passive control stage, natural frequencies of a uni-blade automobile wiper are determined using modal testing. Later, a 3-dimensional model of a wiper blade assembly is developed in multi body system design to investigate the good validation test and agreement of the physical behavior of the system in experiment with finite element analysis. Parametric modification via complex eigenvalue is adopted to predict instability of the wiper blade. In active control level, experimental data collected from the wiper system during its operation. A system identification model named nonlinear auto regressive exogenous Elman neural network (NARXENN) is developed for implying the active controller. A bi-level adaptive-fuzzy controller is brought in whose parameters are tuned simultaneously by a multi objective genetic algorithm (MOGA) to deal with the conflict interests in wiper control problem.     

An Approach to Feed-Forward Controller Design for Underactuated Multibody Systems in the Presence of Uncertainty

The performance of a model-based tracking controller depends on the quality of the underlying model. Especially for flexible multibody systems, the derivation of a suitable model and the subsequent controller design are challenging tasks. In the paper, it is shown how in a straightforward approach a feed-forward controller for a flexible multibody system is designed based on a simplified model which approximates an elastic beam by a combination of rigid beams and force elements. Furthermore, the modelling error due to this harsh simplification is included as uncertainty in the simplified model and considered in the model-based feed-forward controller design using fuzzy arithmetic. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hybrid design of PID controller for four DoF lower limb exoskeleton

In this paper, a method of tuning a proportional-integral-derivative controller for a four degree-of-freedom lower limb exoskeleton using hybrid of genetic algorithm and particle swarm optimization is presented. Transfer function of each link of the lower limb exoskeleton acquired from a pendulum model, was used in a closed-loop proportional-integral-derivative control system, while each link was assumed as one degree-of-freedom linkage. In the control system, the hybrid algorithm was applied to acquire the parameters of the controller for each joint for minimizing the error. The algorithm started with genetic algorithm and continued via particle swarm optimization. Furthermore, a 3-dimensional model of the lower limb exoskeleton was simulated to validate the proposed controller. The trajectory of the control system with optimized proportional-integral-derivative controller via hybrid precisely follows the input signal of the desired. The result of the hybrid optimized controller was compared with genetic algorithm and particle swarm optimization based on statistics. The average error of the proposed algorithm showed the optimized results in comparison with genetic algorithm and particle swarm optimization. Furthermore, the advantages of the hybrid algorithm have been indicated by numerical analysis.     

Stabilization of unknown nonlinear systems using a cognition-based framework

This paper considers an adaptive control method based on a cognition-based framework to stabilize unknown nonlinear systems. In order to fulfill the task of stabilization, neither the information about the systems dynamical structure nor the knowledge about system physical behaviors, but the system states, which are assumed as measurable, are required. The structure of the proposed controller consists of three parts. The first part is based on a recurrent neural network (RNN) to be used for local identification of the unknown nonlinear system in real time. The network can be utilized as system characteristics, which is further used to design the controller within the third part. In the second part, the set of the given input values leading to stable behavior of the closed-loop system will be calculated numerically with a geometrical criterion based on a suitable definition of quadratic stability. In the third part, a suitable control input value is chosen accordingly to a time-relevant criteria from the set of input values generated in the second part of the controller. These three parts and their internal connections are arranged within a so-called cognition framework. The proposed cognitive controller is able to gain useful knowledge (with local validity) and define autonomously a suitable control input with respect to the requirements of the time-relevant criteria. Numerical examples are shown to demonstrate the successful application and performance of the method. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and nonlinear control of a flexible-link manipulator

The problem of modeling and controlling the tip position of a one-link flexible manipulator is considered. The proposed model has been used to investigate the effect of the open-loop control torque profile, and the payload. The control strategy is based on the nonlinear State Dependent Riccati Equation (SDRE) design method in the context of application to robotics and manufacturing systems. In this paper, an experimental test-bed was developed to demonstrate the concept of end-point position feedback on a single-link elastic manipulator, and the control strategy for a single-link flexible manipulator. The controller is designed based on the nonlinear SDRE developed by the authors and applied to a flexible manipulator. The experimental results are compared with conventional PD controller strategy. The results reveal that the nonlinear SDRE controller is near optimal and robustly; and its performance is improved comparing to the PD control scheme.     

Model matching of input/state switched asynchronous sequential machines with the external switching signal

This article investigates the input/state model matching problem of switched asynchronous sequential machines (ASMs) with the external switching signal in the framework of corrective control theory. The considered switched ASM is governed by the external switching signal that arbitrarily changes the mode of the switched ASM, prompting the active submachine into unpredictable state drift. We address the existence condition and design procedure for a proper corrective controller that matches the stable-state behavior of the closed-loop system to that of a reference model under any switching sequence. An illustrative example is provided for demonstrating the synthesis procedure of the proposed corrective controller. Compared with the prior work, the subject of this study is more challenging since rather than manipulated in favor of attaining model matching, the switching signal inflicts adversarial dynamic constraint that must be overcome by the controller.     

输入通道有干扰多变量MRAC系统全局稳定化控制

对具有未建模动态且输入通道存在干扰的动态不确定多输入多输出(MIMO)模型参考自适应控制(MRAC) 系统，仅应用系统的输入输出量测数据给出了一种变结构模型跟踪控制器设计机制.通过辅 助信号和带有记忆功能的正规化信号,并适当选择控制器参数, 所提出的变结构控制 (VSC)能保证闭环系统的全局稳定性,且跟踪误差可调整到任意小.     

A sliding mode control for linear fractional systems with input and state delays

In this paper, a sliding mode control design for fractional order systems with input and state time-delay is proposed. First, we consider a fractional order system without delay for which a sliding surface is proposed based on fractional integration of the state. Then, a stabilizing switching controller is derived. Second, a fractional system with state delay is considered. Third, a strategy including a fractional state predictor input delay compensation is developed. The existence of the sliding mode and the stability of the proposed control design are discussed. Numerical examples are given to illustrate the theoretical developments.     

Modelling and Control of a Hydraulic Actuated Large Scale Manipulator

This contribution deals with the modelling and control of an elastic manipulator. The arm is actuated by a hydraulic ram due to the significant weight. The overall goal is to achieve good tracking of the tip, as well as to reject disturbances, which act on the flexible arm. The controller design is based on two approaches. A flatness‐based feedforward control takes care of the tracking behaviour, and a passivity‐based feedback law stabilizes the trajectories and suppresses the elastic vibrations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Iterative identification and control design using finite-signal-to-noise models

In this paper, a model is said to be validated for control design if using the model-based controller, the closed loop performance of the real plant satisfies a specified performance bound. To improve the model for control design, only closed loop response data is available to deduce a new model of the plant. Hence the procedure described herein involves three steps in each iteration: (i) closed loop identification; (ii) plant model extraction from the closed loop model; (iii) controller design. Thus our criteria for model validation involve both the control design procedure by which the closed loop system performance is evaluated, and the identification procedure by which a new model of the plant is deduced from the closed loop response data. This paper proposes new methods for both parts, and also proposes an iterative algorithm to connect the two parts. To facilitate both the identification and control tasks, the new finite-signal-to-noise (FSN) model of linear systems is utilized. The FSN model allows errors in variables whose noise covariances are proportional to signal covariances. Allowing the signal to noise ratios to be bounded but uncertain, a control theory to guarantee a variance upper bound is developed for the discrete version of this new FSN model. The identification of the closed loop system is accomplished by a new type of q-Markov Cover, adjusted to accommodate the assumed FSN structure of the model. The model of the plant is extracted from the closed loop identification model. This model is then used for control design and the process is repeated until the closed loop performance validates the model. If the iterations produce no such a controller, we say that this specific procedure cannot produce a model valid for control design and the level of the required performance must be reduced.     

An entire strategy for precise system tracking control of a revolving thin flexural link,part II: System output modification

Fast move times and settling times while minimizing the remaining vibrations must be provided by a high performance revolving flexural link. Recent academic work in this area focus on two close related problems. The first priority is concerned with the vibration control while the link is moving. The second problem is the post-slew ending position control. In an attempt to resolve these difficulties, this present paper is a continuation of [1], a regulating reference input technique combined with the aforementioned direct tuning design scheme in order to modify the system output that makes the corresponding closed-loop system of the revolving flexural link for optimal trajectory tracking performance is presented.     

Dynamics modelling and Hybrid Suppression Control of space robots performing cooperative object manipulation

Dynamics modelling and control of multi-body space robotic systems composed of rigid and flexible elements is elaborated here. Control of such systems is highly complicated due to severe under-actuated condition caused by flexible elements, and an inherent uneven nonlinear dynamics. Therefore, developing a compact dynamics model with the requirement of limited computations is extremely useful for controller design, also to develop simulation studies in support of design improvement, and finally for practical implementations. In this paper, the Rigid–Flexible Interactive dynamics Modelling (RFIM) approach is introduced as a combination of Lagrange and Newton–Euler methods, in which the motion equations of rigid and flexible members are separately developed in an explicit closed form. These equations are then assembled and solved simultaneously at each time step by considering the mutual interaction and constraint forces. The proposed approach yields a compact model rather than common accumulation approach that leads to a massive set of equations in which the dynamics of flexible elements is united with the dynamics equations of rigid members. To reveal such merits of this new approach, a Hybrid Suppression Control (HSC) for a cooperative object manipulation task will be proposed, and applied to usual space systems. A Wheeled Mobile Robotic (WMR) system with flexible appendages as a typical space rover is considered which contains a rigid main body equipped with two manipulating arms and two flexible solar panels, and next a Space Free Flying Robotic system (SFFR) with flexible members is studied. Modelling verification of these complicated systems is vigorously performed using ANSYS and ADAMS programs, while the limited computations of RFIM approach provides an efficient tool for the proposed controller design. Furthermore, it will be shown that the vibrations of the flexible solar panels results in disturbing forces on the base which may produce undesirable errors and perturb the object manipulation task. So, it is shown that these effects can be significantly eliminated by the proposed Hybrid Suppression Control algorithm.     

Sampled‐data reliable stabilization of T‐S fuzzy systems and its application

In this article, based on sampled‐data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input‐delay approach, the sampled‐data system is equivalently transformed into a continuous‐time system with a variable time delay. The main objective is to design a suitable reliable sampled‐data state feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger‐based double integral inequality, some new delay‐dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016     

Design of a robust nonlinear controller for a synchronous generator connected to an infinite bus

This article presents a new design of robust finite‐time controller which replaces the traditional automatic voltage regulator for excitation control of the third‐order model synchronous generator connected to an infinite bus. The effects of system uncertainties and external noises are fully taken into account. Then a single input robust controller is proposed to regulate the system states to reach the origin in a given finite time. The designed robust finite‐time excitation controller can refine the system behaviors in convergence and robustness against model uncertainties and external disturbances. The robustness and finite‐time stability of the closed‐loop system are analytically proved using the finite‐time control idea and Lyapunov stability theorem. The suitability and robustness of the designed controller are shown in contrast with two other strong nonlinear control strategies. The main advantages of the proposed controller are as follows: a) robustness against system uncertainties and external noises; b) convergence to the equilibrium point in a given finite time; and c) the use of a single control input. © 2015 Wiley Periodicals, Inc. Complexity 21: 203–213, 2016