Model reference command shaping for vibration control of multimode flexible systems with application to a double-pendulum overhead crane

A double-pendulum overhead crane system exhibits significant nonlinearity and is classified as an under-actuated system, making control more complex. This study focuses on designing a robust shaper to effectively mitigate oscillations in such systems. Two robust shapers, which are Zero Vibration Derivative (ZVD) and Negative Equal-Magnitude (NEM), are considered. These are obtained by convolving two input shapers that are designed based on the hook and payload oscillation frequencies. Matlab simulations are utilized to evaluate the performance of the shapers, using a nonlinear dynamic model of the crane to assess their effectiveness. Simulation results show that the ZVD shaper has a better performance in oscillation reduction, with 81% and 76% reductions for the hook and payload oscillations, respectively. In addition, the ZVD provides the lowest mean average error by achieving 87% and 83% reductions in the hook and payload as compared to the case with an unshaped input. However, the NEM shaper provides less delay in the trolley response.

In this paper, the model reference zero vibration (MRZV) control design is introduced to improve transient performance of robotic manipulators. MRZV consists of a zero vibration (ZV) shaper as the feedforward control while utilizing model reference control to improve robustness and performance under plant model parameter variations. Performance analysis of the MRZV control is given in terms of residual vibration and it is shown that MRZV can tolerate significantly larger plant model variations while maintaining the performance characteristics compared to standard shaper designs such as ZV and ZV and Derivative. A synthesis procedure is provided for the MRZV method to guarantee a prespecified level of residual vibration. Experimental verifications based on a standard cycle time test are carried out on an Adept Technology Cartesian robot. Results confirm the effectiveness of the proposed method.

Inerter-based structural vibration control: A state-of-the-art review

Combustion engineering: Kazutomo Ohtake and Toshitaka Fujiwara, (in Japanese), Corona Publishing Co., Ltd., Tokyo, 1985, v + 215 pp., 2300 yen.

This paper extends input shaping control to one dimensional continua. Unlike discrete systems where the input is shaped only in the temporal domain, temporal and spatial input shaping can produce zero residual vibration in setpoint position control of distributed strings and beams. For collocated and noncollocated boundary control of strings and domain control of strings and pinned beams, the response to step inputs is solved in closed form using delays. For a clamped beam model, a closed form infinite modal series is used. The boundary controlled string can be setpoint regulated using two-pulse Zero Vibration (ZV) and three-pulse Zero Vibration and Derivative (ZVD) shapers but ZVD is not more robust to parameter variations than ZV. Noncolocated ZV and ZVD boundary control enables rigid body translation of a string with zero residual vibration. Domain controlled strings and pinned beams with spatial input distributions that satisfy certain orthogonality conditions (e.g. midspan point load or uniformly distributed load) can be setpoint regulated with shaped inputs. For the cantilevered beam, modal shaping of the input distribution and ZV or ZVD temporal shaping drives the tip to the desired position with zero residual vibration.

This paper proposes a new Piecewise Affine Proportional-Integral-Derivative (PA-PID) controller for cart position tracking and hook and load sway angle suppression of a double pendulum overhead crane (DPOC) system. A Safe Experimentation Dynamics (SED) algorithm is utilized as a model-free optimization tool to find the optimal PA-PID controller parameters such that the integral square of error and input are reduced. The essential feature of the PA-PID controller is that the parameters of proportional, integral and derivative gains are adaptive to the error variations according to the Piecewise Affine (PA) function. Moreover, the proposed PA function is expected to produce better control accuracy than the conventional PID controller. In order to justify the efficacy of the PA-PID controller, a widely known nonlinear model of DPOC plant is considered. The performances of the proposed controller are observed based on the integral square of error and input, and the responses of the cart position, the hook and load sway angle and the control input. The numerical results verify that the proposed PA-PID controller yields higher control accuracy than the conventional PID controller of DPOC system.

A novel energy-coupling-based control method for under-actuated double-pendulum overhead cranes with initial control force constraint is proposed in this article. The significant feature of the designed controller is its superior control performance as well as its strong robustness with respect to parameter variations and external disturbances. By incorporating a smooth hyperbolic tangent function into the control law, the proposed controller guarantees soft start of the trolley. Moreover, to improve the transient performance of the crane system, coupling behavior among the trolley movement, the hook swing, and the payload swing is enhanced by introducing a generalized payload horizontal-displacement signal. Lyapunov techniques and LaSalle’s invariance theorem are utilized to prove the stability of the designed closed-loop system. Simulation results demonstrate that the new energy-coupling control method achieves superior control performance and strong robustness over different payload masses, cable lengths, desired positions, and external disturbances with reduced initial control force.

The connection of two building structures with dampers is one of effective vibration control systems. In this vibration control system, both buildings have to possess different vibration properties in order to provide a higher vibration reduction performance. In addition to such condition of different vibration properties of both buildings, the connecting dampers also play an important role in the vibration control mechanism. In this paper, the effect of nonlinearity of connecting dampers on the vibration control of connected building structures is investigated in detail. A high-damping rubber damper and an oil damper with and without relief mechanism are treated. It is shown that, while the high-damping rubber damper is effective in a rather small deformation level, the linear oil damper is effective in a relatively large deformation level. It is further shown that, while the oil dampers reduce the response in the same phase as the case without dampers, the high-damping rubber dampers change the phase. The merit is that the high-damping rubber can reduce the damper deformation and keep the sufficient space between both buildings. This can mitigate the risk of building pounding.

Nowadays, landing gears used in aircraft are the basic systems that carry the weight of aircraft systems and provide them to move on the ground. During the landing of aircraft, big and sudden vibrations occur as soon as the wheels come into contact with the runway. This situation negatively affects human safety, comfort and also the life of the landing gear system. Therefore, it is important to keep this vibration at permissible levels. This paper presents an improved vibration control method that controls the amplitudes of vibrations of landing systems. This paper presents proposed vibration control method that controls the angular position variables of the landing gear mechanism to control the vibrations occurring during landing. For different runway conditions and 200 km/h landing speed, the angular joint variables of the landing gear mechanism links are controlled using standard controller and a proposed neural controller structure. The simulation results are shown that the proposed neural controllers have better performance at vibration control of landing systems during landing.

Vibratory phenomena have always surrounded human life. The need for more knowledge and domain of such phenomena increases more and more, especially in the modern society where the human-machine integration becomes closer day after day. In that context, this work deals with the development and practical implementation of a hybrid (passive-active/adaptive) vibration control system over a metallic beam excited by a broadband signal and under variable temperature, between 5 and 35°C. Since temperature variations affect directly and considerably the performance of the passive control system, composed of a viscoelastic dynamic vibration neutralizer (also called a viscoelastic dynamic vibration absorber), the associative strategy of using an active-adaptive vibration control system (based on a feedforward approach with the use of the FXLMS algorithm) working together with the passive one has shown to be a good option to compensate the neutralizer loss of performance and generally maintain the extended overall level of vibration control. As an additional gain, the association of both vibration control systems (passive and active-adaptive) has improved the attenuation of vibration levels. Some key steps matured over years of research on this experimental setup are presented in this paper.

Considering the problems of model uncertainties, higher harmonics, uncertain boundary conditions, external excitations, and system time delay in practical vibration control system, a novel active vibration control method is proposed to suppress the vibration of a thin plate structure with acceleration sensor and piezoelectric bimorph actuator in this paper. First, a nonlinear extended state observer (NESO)-based controller is designed to ensure the anti-disturbance performance of the structural vibration control system. Then, an enhanced differentiator-based time delay compensation method is introduced to improve the vibration suppression performance of the NESO-based controller. A real time hardware-in-the-loop benchmark for an all-clamped piezoelectric thin plate is designed to verify and compare the performance of the developed controller against conventional ESO-based methods (linear ESO with/without time delay compensation, NESO without time compensation). The best vibration suppression and disturbance rejection performance of the proposed NESO-based controller with an enhanced time delay compensator is verified in the comparative experimental results. This work is able to provide practitioners with vital guidance in designing active vibration control system in the presence of disturbances and time delay.

Simulink® implementation and industrial test of Input Shaping techniques

Shaping command input is performed for reducing residual vibrations in motion control of dynamical structures. System inputs are changed so that the structure reaches to planned motion in minimum duration without residual oscillation. Shaping input is obtained by convolving desired input with an impulse sequence. Main goal of the input shaper design is to define impulse amplitudes and their instants from the dynamical behavior of uncontrolled response. Zero Vibration (ZV), Zero Vibration and Derivative (ZVD) and Extra Insensitive (EI) are the most common shaper types. Improving the robustness respect to modeling errors requires more impulses. These increase control duration and make difficult to solve constraint equations directly. Required parameters can be determined from the derivation of constraint equations. This paper presents Three-Step (TS) input shaping technique. A solution space for three-impulse shaping is given including both positive and negative shapers. It is shown here that ZVD and EI shapers are the special solution points in TS shaping space. The duration of the shaper less or more than ZVD's can be obtained in the defined space. Some of the new shapers give better robustness than ZVD. Experimental results from a prototype planar crane system are used to support the numerical results.

Input shaping technique is used to improve the performance of many flexible systems. Employing specified train of impulses convolved with a reference command can effectively reduce residual vibrations. Zero vibration, zero vibration derivative and specified insensitive or extra insensitive, and zero vibration derivative-derivative shapers are wellknown types of input shapers. These shapers improve the robustness of the system with respect to modelling errors. In this article, a coherent input shaping scheme with all positive threeimpulse sequences is developed, which is preferable to derivative shaper types. The proposed method is used for damping the tubular step motor vibrations. The method allows generating the impulse amplitudes without additional derivative constraints. The technique is also evaluated by analysing the robustness. Experimental results show the efficiency of the proposed method.

This paper investigates the implementation of supplemental vibration control systems (VCS) in base isolated (BI) structures, to improve their dynamic performance. More specifically, the aim of the VCS is to reduce the base displacement demand of BI structures, and at the same time mitigate the superstructure seismic responses. The purpose of the examined VCS is dual, and for this reason a multi-objective optimization methodology is formulated for the design of the VCS. The examined vibration absorbers include modifications of the KDamper concept. The KDamper is an extension of the traditional Tuned Mass Damper (TMD), and introduces a negative stiffness (NS) element to the additional oscillating mass of the TMD. The generated NS force is exactly in phase with the inertia force of the added mass, thus, artificially amplifying it. This way, lighter configurations are possible with an enhanced damping behavior. These VCS are designed based on engineering criteria and manufacturing constraints, while the excitation input used in the multi-objective optimization procedure is selected from a dataset of artificial accelerograms, designed to be spectrum-compatible with the EC8 design acceleration response spectrum. The effectiveness of the examined VCS is also assess with real near-fault earthquake records, and a comparison is performed with TMD-based VCS having 50 times larger additional masses. The numerical results demonstrate the superiority of the KDamper-based VCS in improving the dynamic behavior of BI structures over other mass-related systems (TMD).