Stabilization and shape control of a 1D piezoelectric Timoshenko beam

In this paper we show how to perform stabilization and shape control for a finite dimensional model that recasts the dynamics of an inflatable space reflector in port-Hamiltonian (pH) form. We show how to derive a decentralized passivity-based controller which can be used to stabilize a 1D piezoelectric Timoshenko beam around a desired shape. Furthermore, we present simulation results obtained for the proposed decentralized control approach.     

Optimal control of vibrations of a dynamic Gao beam in contact with a reactive foundation

In this paper, we investigate the optimal control of vibrations of a nonlinear viscoelastic beam, which is acted upon by a horizontal traction, that may come in contact with a reactive foundation underneath it. By the Dubovitskii and Milyutin functional analytical approach, we derive the Pontryagin maximum principle of the system governed by the Gao beam equation. And the first-order necessary optimality condition is presented for the optimal control problem in fixed final horizon case. Finally, we also sketch the numerical solution based on the obtained theoretical results.     

Active noise control of flexible linkage mechanism with piezoelectric actuators

An active noise control method for flexible linkage mechanism systems with piezoelectric actuators and strain gauge sensors is studied. By employing a set of wave number transformations on the original equations of motion of the flexible linkage mechanisms, a new set of equations of motion is obtained, in which the unknown variables can describe the structural acoustic radiation level of the mechanism system directly. On the basis of the new equations, the active noise control of the flexible linkage mechanism system with piezoelectric actuators is discussed. Firstly, the optimal control forces are determined based on the optimal control theory. Secondly, the controller of the system that consists of the output feedback and the disturbance feed-forward control laws is presented. Simulations show that the method presented in this paper is valid.     

Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters

Considering the randomness of physical parameters of structural material, geometric dimensions of active bars and passive bars, applied loads and control forces simultaneously, the optimization of active bar’s placement and feedback gains for the vibration control of intelligent truss structures are studied in this paper. Firstly, the performance function is developed based on the maximization of dissipation energy due to control action. Then, the optimal mathematical model with the reliability constraints on dynamic stress and displacement response is built. The numerical feature of dynamic response based on probability of intelligent structure is developed. Finally, a planar intelligent truss structure is used as an example to demonstrate the rationality and validity of the presented model and approach in structural active vibration control.     

Design and robust optimal control of smart beams with application on vibrations suppression

This paper presents the design of a vibration control mechanism for a beam with bonded piezoelectric sensors and actuators and an application of the arising smart structure for vibrations suppression. The mechanical modeling of the structure and the subsequent finite element approximation are based on Hamilton's principle and classical engineering theory for bending of beams in connection with simplified modeling of piezoelectric sensors and actuators. Two control schemes LQR and H₂ are considered. The latter robust controller takes into account uncertainties of the dynamical system and moreover incompleteness of the measured information, it therefore leads to applicable design of smart structures. The numerical simulation shows that sufficient vibration suppression can be achieved by means of the proposed general methods.     

Numerical simulations of cantilever beam response with saturation control and full modal coupling

Numerical simulations of the response of a uniform, cantilever beam subjected to a base excitation are performed. A saturation absorber is implemented to control the beam response. In previous investigations of similar configurations, the inertial and structural properties of the piezoelectric actuators have been neglected, resulting in an analytical model of a uniform beam. This investigation includes the nonuniformities in the beam properties that are introduced when piezoelectric actuators are bonded to the uniform beam. The resulting coupling between uniform, cantilever beam modes is fully included in the analytical model. It is shown that this modal coupling has a significant effect on the beam response, which is not present when modal coupling is neglected.     

Iterative learning control of a fully flexible valve actuation system for non-throttled engine load control

This paper presents the application of a fully flexible valve actuation system for non-throttled load control of an internal combustion engine. A novel camless valve actuation system with a unique hydro-mechanical internal feedback mechanism which simplifies the external control design is first introduced. All the critical parameters describing the engine valve event, i.e., lift, timing, duration and seating velocity, can be continuously varied by controlling the triggering timings of three two-state valves. Initial testing of a prototype experimental setup reveals that the performance of the system (transient tracking and steady-state variability) is influenced purely by the state of the system when the internal feedback mechanism is activated. This feature motivates the development of a cycle-to-cycle learning-based external control for activating the internal feedback mechanism based on the desired valve profile characteristics and the system state. To verify the proposed control methodology, it is implemented on the experimental system to track reference trajectories for the various valve event parameters corresponding to the non-throttled load control of an engine during the U.S. Federal Test Procedure (FTP) urban driving cycle. Vehicle load demand analysis is used to compute the desired engine speed and torque requirements. Detailed dynamic valve flow simulations assuming full flexibility of the engine valve event parameters help to calculate the required trajectory of all these parameters to satisfy the speed and torque requirements without the use of a throttle. The experimental results show that the proposed framework, i.e., the valve actuation system and the external control methodology, is able to provide excellent performance even during the most aggressive transient operating conditions.     

Optimal tracking control of a flexible hub–beam system with time delay

In this paper, a new technique of time-delay compensation is proposed for active control of a flexible hub–beam system. The first-order approximation coupling (FOAC) model proposed recently for dynamics of hub–beam systems is used to verify the applicability of this technique. The FOAC model is first linearized to obtain a linearized equation. The linearized equation with time delay is then transformed into a standard form with no time delay by a particular integral transformation. The time-delay controller is designed based on this standard equation using the classical optimal tracking control theory. Since the controller is a function of modal coordinates, a modal filter is presented to estimate the modal coordinates from physical sensor measurements. The effectiveness of the proposed technique for time delay is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in instability of the control system if it is not compensated in control design. The proposed time-delay controller is effective in controlling the system even when the maximum time delay for stability without time-delay compensation is greatly exceeded. Moreover, for the system without time delay, the proposed time-delay controller may possibly obtain much better control effectiveness than the controller without time delay.     

Optimal control of distributed bilinear systems

The optimal control problem for a bilinear distributed parameter system subject to a quadratic cost functional is solved. It is shown that the optimal control is given by a convergent power series in the state with tensor coefficients.     

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances. The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms. Based on the internal model principle, a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances. According to the sensitivity approach, the optimal tracking control law for the ith nonlinear subsystem can be obtained. The optimal tracking control law for the nonlinear large-scale systems can be obtained. A numerical simulation shows that the method is effective.     

Distributed adaptive neural network control for a class of heterogeneous nonlinear multi-agent systems subject to actuation failures

In this paper, the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems on directed graph is addressed. Each follower is modelled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics, disturbances and actuator failures. Cooperative fault tolerant neural network tracking controllers with online adaptive learning features are proposed to guarantee that all agents synchronise to the trajectory of one leader with bounded adjustable synchronisation errors. With the help of linear quadratic regulator-based optimal design, a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology, one virtual matrix and some design parameters. Of particular interest is that if the control gain is selected appropriately, the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not. Furthermore, the fault detection and isolation are not needed to implement. Finally, a simulation is given to verify the effectiveness of the proposed method.     

Modeling and control of an atomic force microscope using a piezoelectric tuning fork for force sensing

This paper investigates modeling and control issues associated with an atomic force microscope which uses a piezoelectric tuning fork for atomic force sensing. In the modeling part, the dynamics of piezoelectric tuning fork and its atomic interaction with the test sample via the scanning tip are physically characterized. The modeling results explain not only the atomic force sensing mechanism but also the important characteristics observed in experimental frequency responses. In the control part, an LTR controller is designed to maximize the controller bandwidth and yet maintain robustness against unmodeled dynamics and different operating conditions. Scanning results indicate that the LTR controller exhibits superior performance than a conventional PI controller.     

Maximum principle for optimal control of vibrations of a dynamic Gao beam in contact with a rigid foundation

In our preceding paper, we studied an optimal control problem of vibrations of a dynamic Gao beam in contact with a reactive foundation and derived the Pontryagin maximum principle for the controlled system in fixed final horizon case. As a follow-up, in this paper, we focus on the investigation of the Gao beam that may come in contact with a rigid foundation underneath it. In this case, the nonlinear viscoelastic beam equation is equipped with the Signorini condition. By the Dubovitskii and Milyutin functional analytical approach, we investigate the new optimal control problem with multiple inequality constraints and present further original results of current interests.     

带有持续扰动的时滞非线性大系统的最优跟踪控制

研究具有外界持续扰动的时滞非线性大系统的无静差最优跟踪控制问题.将时滞非线性大系统分解为带有互联项的N个时滞非线性子系统,基于内模原理对子系统构造扰动补偿器,将带有外部持续扰动的子系统化为无扰动的增广系统.通过灵敏度法求解不含时滞的两点边值问题,得到子系统的最优跟踪控制律,截取最优跟踪控制律的前N项作为次优控制律来近似系统的最优控制律.仿真实例表明了该设计方法的有效性.     

Compensation of hysteresis in piezoelectric actuator with iterative learning control

This paper presents the application of iterative learning control (ILC) to compensate hysteresis in a piezoelectric actuator. The proposed controller is a hybrid of proportional-integral-differential (PID) control, whose main function is for trajectory tracking, and a chatter-based ILC, whose main function is for hysteresis compensation. Stability analysis of the proposed ILC is presented, with the PID included in the dynamic of the piezoelectric actuator. The performance of the proposed controller is analysed through simulation and verified with experiment with a piezoelectric actuator.     

Optimal control of switching systems

This paper considers an optimal control problem for a switching system. For solving this problem we do not make any assumptions about the number of switches nor about the mode sequence, they are determined by the solution of the problem. The switching system is embedded into a larger family of systems and the optimization problem is formulated for the latter. It is shown that the set of trajectories of the switching system is dense in the set of trajectories of the embedded system. The relationship between the two sets of trajectories (1) motivates the shift of focus from the original problem to the more general one and (2) underlies the engineering relevance of the study of the second problem. Sufficient and necessary conditions for optimality are formulated for the second optimization problem. If they exist, bang-bang-type solutions of the embedded optimal control problem are solutions of the original problem. Otherwise, suboptimal solutions are obtained via the Chattering Lemma.     

Optimal control of container cranes

A dynamical model of container cranes is derived by using Lagrange's equation. When a ship is loaded or unloaded with containers, the total motion of the container load is divided into five fundamental sections. For each fundamental type of motion, the optimal control is calculated such that the corresponding trajectory satisfies the specified boundary conditions and that the swing of the container load during the transfer is minimized. A new algorithm which is employed for computing the optimal control is explained in detail. Some results of numerical computation are also shown.     

Optimal adaptive scheduling and control of beer membrane filtration

An adaptive optimal scheduling and controller design is presented that attempts to improve the performance of beer membrane filtration over the ones currently obtained by operators. The research was performed as part of a large European research project called EU Cafe with the aim to investigate the potential of advanced modelling and control to improve the production and quality of food. Significant improvements are demonstrated in this paper through simulation experiments. Optimal scheduling and control comprises a mixed integer non-linear programming problem (MINLP). By making some suitable assumptions that are approximately satisfied in practice, we manage to significantly simplify the problem by turning it into an ordinary non-linear programming problem (NLP) for which solution methods are readily available. The adaptive part of our scheduler and controller performs model parameter adaptations. These are also obtained by solving associated NLP problems. During cleaning stages in between membrane filtrations enough time is available to solve the NLP problems. This allows for real-time implementation.     

Dynamics and control of a novel 3-DOF parallel manipulator with actuation redundancy

This paper deals with the dynamics and control of a novel 3-degrees-of-freedom （DOF） parallel manipulator with actuation redundancy. According to the kinematics of the redundant manipulator, the inverse dynamic equation is formulated in the task space by using the Lagrangian formalism, and the driving force is optimized by utilizing the minimal 2-norm method. Based on the dynamic model, a synchronized sliding mode control scheme based on contour error is proposed to implement accurate motion tracking control. Additionally, an adaptive method is introduced to approximate the lumped uncertainty of the system and provide a chattering-free control. The simulation results indicate the effectiveness of the proposed approaches and demonstrate the satisfactory tracking performance compared to the conventional controller in the presence of the parameter uncertainties and un-modelled dynamics for the motion control of manipulators.     

Extended state observer-based motion synchronisation control for hybrid actuation system of large civil aircraft

Hybrid actuation system with dissimilar redundant actuators, which is composed of a hydraulic actuator (HA) and an electro-hydrostatic actuator (EHA), has been applied on modern civil aircraft to improve the reliability. However, the force fighting problem arises due to different dynamic performances between HA and EHA. This paper proposes an extended state observer (ESO)-based motion synchronisation control method. To cope with the problem of unavailability of the state signals, the well-designed ESO is utilised to observe the HA and EHA state variables which are unmeasured. In particular, the extended state of ESO can estimate the lumped effect of the unknown external disturbances acting on the control surface, the nonlinear dynamics, uncertainties, and the coupling term between HA and EHA. Based on the observed states of ESO, motion synchronisation controllers are presented to make HA and EHA to simultaneously track the desired motion trajectories, which are generated by a trajectory generator. Additionally, the unknown disturbances and the coupling terms can be compensated by using the extended state of the proposed ESO. Finally, comparative simulation results indicate that the proposed ESO-based motion synchronisation controller can achieve great force fighting reduction between HA and EHA.