Rotary Pendulum Research Articles

Broadband vibration energy harvester based on nonlinear magnetic force and rotary pendulums

A broadband vibration energy harvester based on nonlinear magnetic force and rotary pendulums is proposed in this paper. The harvester is mainly composed of a magnetoelectric transducer and a rotary pendulum fixed with four permanent magnets. In order to improve the working bandwidth of the harvester, two pairs of permanent magnets are added in the middle of the rotary pendulum by using magnetic nonlinearity. The mechanical–magnetic–electrical analytical model of the harvester is established, and the theoretical value obtained by the model is basically consistent with the experimental value. The results show that the harvester has a strong nonlinearity through the magnetic force. When the acceleration is 0.4 g, some typical testing results are as follows: the resonant frequency is 19 Hz, maximum peak–peak voltage is 94.1 V, half power bandwidth is 15.8 Hz, center frequency is 26.9 Hz, and the ratio of half power bandwidth to the center frequency is 58.73.

Methodology of robust inverted pendulum controllers on a vehicle

In the theory of controllers, the simple and inverted pendulum play an important role due to the equations that result from them, which imply non-linearities and perturbations, thus, in this article, a brief classification of inverted pendulums is presented: inverted pendulum, inverted double pendulum, inverted rotary pendulum (Furuta pendulum). Subsequently, a mathematical model of the inverted pendulum is described through the deduction of the equations of motion that represent the dynamics of the system. Robust control is presented that allows expanding the richness of the mathematical equations, for this case, a control with output feedback is presented and applied to the inverted pendulum to control the unstable dynamics of this model. The results are compared with a post placement control and a robust control using a norm that analyses the characteristics of the system.

Anti-swing radial basis neuro-fuzzy linear quadratic regulator control of double link rotary pendulum

In this article, a radial basis neuro-fuzzy linear quadratic regulator controller is developed for the anti-swing control of a double link rotary pendulum system. The objective of this work is to study the radial basis neuro-fuzzy linear quadratic regulator controller and to compare it with a fuzzy linear quadratic regulator and the linear quadratic regulator controllers. In the proposed radial basis neuro-fuzzy linear quadratic regulator controllers, the positions and velocities of state variables multiplied by their linear quadratic regulator gains are trained using two radial basis neural networks architecture. The output of the two radial basis neural networks is used as the input variables of the fuzzy controller. The novel architecture of the radial basis neuro-fuzzy controller is developed in order to obtain better control performance than the classical adaptive neuro-fuzzy controller. To determine the control performance of the anti-swing controllers, different control parameters are computed. According to the comparative results, the anti-swing radial basis neuro-fuzzy linear quadratic regulator controller yields improved results than fuzzy linear quadratic regulator and linear quadratic regulator. Furthermore, the performance of the three controllers developed was compared based on robustness analysis under external force disturbance. The results obtained here indicate that the anti-swing radial basis neuro-fuzzy linear quadratic regulator controller product has better performance than other controllers in terms of vibration suppression ability.

Stabilization of energy level sets of underactuated mechanical systems exploiting impulsive braking

Recent investigations of underactuated systems have demonstrated the benefits of control inputs that are impulsive in nature. Here we consider the problem of stabilization of energy level sets of underactuated systems exploiting impulsive braking. We consider systems with one passive degree-of-freedom (DOF) and the energy level set is a manifold where the active coordinates are fixed and the mechanical energy equals some desired value. A control strategy comprised of continuous inputs and intermittent impulsive braking inputs is presented. The generality of the approach is shown through simulation of a three-DOF Tiptoebot; the feasibility of implementation of impulsive control using standard hardware is demonstrated using a rotary pendulum.

Guaranteed cost estimation and control for a class of nonlinear systems subject to actuator saturation

The problems of guaranteed cost estimation (GCE) and guaranteed cost control (GCC) concern designing a state observer or a controller, respectively, such that some performance is maintained below an upper bound. This paper provides a matrix inequality-based observer/controller design procedure to perform GCE and GCC in a class of nonlinear systems affected by actuator saturation. In particular, this class of systems corresponds to those for which the origin of the state space is an equilibrium point when null inputs are considered, and the nonlinearity is differentiable with respect to the state and linear with respect to the saturated input. Simulation results obtained using a numerical example and a rotational single-arm inverted pendulum are used to illustrate the effectiveness of the proposed design procedure.

A Study of Anti-swing Fuzzy LQR Control of a Double Serial Link Rotary Pendulum

In this work, a Fuzzy Linear Quadratic Regulator (FLQR) is developed for the anti-swing control problem of a Double Serial Link Rotary Pendulum (DSLRP) system. The main objective of this paper is to study the anti-swing FLQR controller and compare it with the classical LQR controller. A dynamic mechanical model of the DLRP was simulated numerically in the SimMechanics toolbox/MATLAB. This model can be defined mathematically as the single input and multiple output non-linear dynamic equations. To verify the performance of both anti-swing controllers, different time-domain control specifications are computed. Moreover, to show the controllers performance, simulation and experiments results are given and compared. According to the comparative results, the FLQR anti-swing controller produces better results than classical LQR in term of time-domain control specifications. Moreover, the controllers’ dynamic responses were compared according to robustness analysis in the presence of external force disturbance. The results obtained here indicate that the FLQR anti-swing controller product better performance than others in term of vibration suppression capability.

Study of dynamics of rotational centrifugal pendulum vibration absorbers based on tautochronic design

A method for designing the key parameters of rotational centrifugal pendulum vibration absorbers is proposed herein. The vibration equations of the pendulum and rotor were established by utilizing Lagrange’s equations. It was found that there were two kinds of rotational centrifugal pendulum vibration absorbers (CPVAs): a linear rotational CPVA and a nonlinear rotational CPVA, which both behaved approximately as linear oscillators. The choice of the linear rotational coefficient and the nonlinear rotational coefficient (only for the nonlinear rotational CPVA) was analyzed, and the selection of the tuning order and trajectories of the centroid of the pendulum was investigated based on tautochronic design theory. In this study, the time variables were transformed to angle variables in the vibration equations. The parameters in the equations were then non-dimensionalized, and the equations were decoupled. Finally, the vibration responses of the pendulum and rotor were solved using the harmonic balance method. The results demonstrated that the linear rotational CPVA designed by utilizing tautochronic theory provided a better damping effect than the nonlinear rotational and non-rotational CPVAs. Furthermore, the linear rotational CPVA could decrease the impact effect on the rotor by adjusting the linear rotational angle and ensure its damping performance.

Hierarchical adaptive control of self-stabilizing electromechanical systems using artificial-immune self-tuning mechanism for state weighting-factors

This article presents a novel self-adaptive linear-quadratic-regulator (LQR) architecture to improve the robustness of self-stabilizing electromechanical systems against exogenous disturbances. The main contribution of this article is to formulate a nonlinear-type artificial-immune adaptation mechanism that dynamically adjusts the state-weighting-factors of LQR’s quadratic-performance-index online. The Riccati-equation solver uses these updated state-weighting-factors to yield time-varying state-feedback gains. This hierarchical control procedure uses immunological computations to indirectly alter the LQR gains, which helps in flexibly reconfiguring the control trajectory under disturbances. The performance of the proposed immune-adaptive LQR is benchmarked against a conventional adaptive LQR and a fixed-gain LQR by conducting software simulations on the nominal model of the QNET rotary pendulum system. Credible real-time experiments are also conducted on the QNET rotary pendulum’s hardware setup to analyze each controller’s efficacy in the physical environment. The simulation and experimental results validate the superior disturbance-rejection capability of the proposed controller under every testing scenario.

An alternative approach for measuring yield stress and its application in Carbopol microgel

An innovative experimental apparatus for the direct measurement of yield stress was conceived and realized. It is based on a torsion pendulum equipped with a magnetic dipole and a rotating cylinder immersed in the material to be investigated. The pendulum equilibrium state depends on the mechanical torque applied due to an external magnetic induction field, elastic reaction of the suspension wire, and shear yield stress. Experimental results are reported showing that the behavior of the pendulum rotation angle, in different equilibrium conditions, provides evidence of the yield stress presence and enables its evaluation by equilibrium equations. The dependence on time of the equilibrium approach was also studied, contributing to shed light on the relaxation effect in the transition from a fluid-like to solid-like behavior, as well as on the eventual thixotropic effects in non-Newtonian fluids. The validity of the proposed technique and related experimental apparatus was tested in aqueous Carbopol solutions, with different weight percentages. The linear procedure, combined with the effectiveness and reliability of the proposed experimental method, candidates it to be used for the study of peculiar behaviors of other yield stress complex fluid such as blood, crude waxy oils, ice slurries, and coating layer used in the food industry and also for fault sliding in geodynamics.

Stable Learning-Based Tracking Control of Underactuated Balance Robots

We present a Gaussian process (GP)-based tracking control of underactuated balance robots in which an actuated subsystem is required to follow a desired trajectory, while an unactuated, unstable subsystem needs to be kept balanced. The GP models are used to capture the coupling effects between the actuated/unactuated subsystems through a constructed balance equilibrium manifold (BEM). Optimization-based algorithm is used to obtain the BEM estimation. The control design takes advantage of the structural property of the robot dynamics and is built on the GP models with a data selection algorithm. Stability analysis is given to guarantee the tracking control performance. The control design and comparison with other controllers are demonstrated through experiments on a rotary pendulum.

Extended state observer based robust sliding mode control for fourth order nonlinear systems with experimental validation

It is commonly known that the design of control is difficult for the systems with non-minimum phase behavior, the coupling between the controlled variables and integral instability. The paper presents such a typical class of nonlinear system and propose a new technique generalized extended state observer-based sliding mode decoupling control. The proposed control algorithm is also able to compensate for the matched and mismatched uncertainties encountered in such nonlinear non-minimum phase systems. The decoupling control approach is used to decouple the entire system framework into subsystems. The sliding surface of the individual subsystem was composed using the estimated states of GESO. The proposed technique can nullify the effect of external disturbances, parametric uncertainties and unmodelled dynamics due to the inclusion of disturbance compensation gain in the control law. The proposed methodology enables the system to accomplish asymptotic stability and better dynamic response with lesser IAE and ITAE values than existing decoupling control strategies. An experimental application of the proposed technique to Quanser’s rotary pendulum module is investigated.

Minimum-time feedback control of a rotary pendulum using deep learning

Minimum-time feedback control of a rotary pendulum using deep learning

Self-tuning state-feedback control of a rotary pendulum system using adjustable degree-of-stability design

This paper formulates an original hierarchical self-tuning control procedure to enhance the disturbance-rejection capability of under-actuated rotary pendulum systems against exogenous disturbances. The conventional state-feedback controllers generally make a trade-off between the robustness and control effort in a closed-loop system. To combine the aforementioned characteristics into a single framework, this paper contributes to develop and augment the baseline Linear-Quadratic-Regulator (LQR) with a novel “adjustable degree-of-stability design” module. This augmentation dynamically relocates the system's closed-loop poles in the stable (left-half) region of the complex plane by dynamically adjusting a single hyper-parameter that modifies the constituents of LQR's performance index. The hyper-parameter is adaptively modulated online via a pre-calibrated hyperbolic-secant-function that is driven by state-error variables. The performance of the proposed adaptive controller is benchmarked against fixed-gain controllers via credible hardware experiments conducted on the standard QNET Rotary Pendulum setup. The experimental outcomes indicate that the proposed controller significantly enhances the system's robustness against exogenous disturbances and maintains its stability within a broad range of operating conditions, without inducing peak servo requirements.

Adaptive State-space Control of Under-actuated Systems Using Error-magnitude Dependent Self-tuning of Cost Weighting-factors

This article methodically constructs a novel adaptive self-tuning state-space controller that enhances the robustness of under-actuated systems against bounded exogenous disturbances. The generic Linear-Quadratic-Regulator (LQR) is employed as the baseline controller. The main contribution of this article is the formulation of a hierarchical online gain-adjustment mechanism that adaptively modulates the weighting-factors of LQR’s quadratic-performance-index by using pre-calibrated continuous hyperbolic scaling functions. The hyperbolic scaling functions are driven by the magnitude of system’s state-error variables. This augmentation dynamically updates the solution of the Matrix-Riccati-Equation which modifies the state-feedback gains after every sampling interval. The efficacy of the proposed adaptive controller is validated by conducting hardware-in-the-loop experiments on QNET Rotary Pendulum setup. The experimental outcomes show that the proposed adaptive control scheme yields stronger damping against oscillations and faster error-convergence rate, while maintaining the controller’s asymptotic-stability, under the influence of parametric uncertainties.

Normal-force dependant friction in centrifugal pendulum vibration absorbers: Simulation and experimental investigations

A model of the normal-force dependant friction loss between the rotor and pendula is developed for bifilar centrifugal pendulum vibration absorbers (CPVAs). The normal-force is dominantly dependant on the rotor rotational velocity but also dependant on the pendulum path. Simulation results of the pendulum with the proposed normal-force friction model agree well with novel experimental results. Order-response simulations of the rotor-CPVA model with the proposed friction model reveal accuracy improvements on the prediction of the rotor oscillation amplitude at different rotational velocities in comparison to existing friction formulations. Derivation of the equations of motion of the rotor-CPVA is performed by Kane’s method and solved numerically. The developed experimental setup is used to validate the model parameters such as friction coefficients, path parameters and relative pendulum rotation without necessitating a special test-apparatus other than standard vibration measurement equipment. CPVAs are commonly used to reduce torsional vibration created by reciprocating engines. To reduce emissions, heavy-duty vehicles manufactures are downsizing and downspeeding the combustion engine while maintaining the power output. Unfortunately, this gives rise to increased torsional vibration in the powertrain. The CPVA is a device that can reduce the torsional vibration and thus help fulfill environmental goals.

Influence of functional group content in hydroxyl-functionalized urethane methacrylate oligomers on the crosslinking features of clearcoats

Crosslinking characteristics and surface mechanical properties of radical and urethane dual-curable clearcoats were investigated by changing quantities of C=C bonds and OH groups in hydroxyl-functionalized urethane methacrylate oligomer (HFUMO) resins. The isocyanate blocked with a thermal radical initiator (BL-Tri-cHD) was utilized as a hybrid dual-curable thermal crosslinker to expedite the crosslinking of the main resin. The dual reactions between various HFUMO resins and BL-Tri-cHD were efficiently monitored via Fourier transform infrared spectroscopy to measure the peaks before and after curing. The influence of each functional group (C=C bond or OH group) in HFUMO on the initiation and development of crosslinking in dual-curable clearcoats was investigated by real-time measurements using rotational rheometer and rigid body pendulum tester. Temperature-dependent mechanical properties of cured films were confirmed through dynamic mechanical analysis. The surface mechanical properties of cured clearcoat films were also evaluated via the nanoindentation and nanoscratch tests, demonstrating the variation in surface resistance with respect to the C=C bond content and the OH value. Thus, the low-temperature curing and desired mechanical properties of clearcoats can be optimized by adjusting the content of the functional groups in a HFUMO and using a dual-curable crosslinker to simultaneously generate both radical and urethane crosslinking reactions.

Intelligent Swing-Up and Robust Stabilization via Tube-based Nonlinear Model Predictive Control for A Rotational Inverted-Pendulum System

The purpose of this paper is to introduce a new robust nonlinear model-based predictive control scheme applied to a rotational inverted-pendulum system. The rotational pendulum is composed by a mechanical arm attached to a free-motion pendulum (orthogonal to the arm), namely Furuta Pendulum. In principle, a Fuzzy controller enables the robotic arm bar to lift the rotational pendulum through oscillatory swing-up motion up to automatically achieve the upper equilibrium position in a prescribed stabilizing operation range. After the pendulum reaches the operating range, an intelligent control bypass system allows the transition between the swing-up motion controller and a robust predictive controller to maintain the angular position of the pendulum around the upward critical position. To achieve robust performance, a centralized control framework combines a triplet of control actions. The first one compensates for disturbances using the regulation trajectory ?feedforward control. The second control action corrects errors produced by modelling mismatch. The third controller assures robustness on the closed-loop system whilst compensating for deviations of the state trajectories from the nominal ones (i.e, disturbance-free). The control strategy provides robust feasibility despite constraints on the arm bar and pendulum's actuators are met. Such constraints are calculated on-line based on robust positively invariant sets characterised by polytopic sets (tubes). The proposed controller is tested in a series of simulations, and experimentally validated on a high-fidelity simulation environment including a rotational inverted-pendulum built for educational purposes. The results show that robust control performance is strengthened against disturbances of the closed-loop system benchmarked to inherently-robust linear and nonlinear predictive controllers.

Surface waves along liquid cylinders. Part 1. Stabilising effect of gravity on the Plateau–Rayleigh instability

We study the shape and the geometrical properties of sessile drops with translational invariance (namely ‘liquid cylinders’) deposited upon a flat superhydrophobic substrate. We account for the flattening effects of gravity on the shape of the drop using a pendulum rotation motion analogy. In the framework of the inviscid Saint-Venant equations, we show that liquid cylinders are always unstable because of the Plateau–Rayleigh instability. However, a cylindrical drop deposited upon a superhydrophobic non-flat channel (here, wedge-shaped channels) is stabilised beyond a critical cross-sectional area. The critical threshold of the Plateau–Rayleigh instability is analytically computed for various profiles of the channel. The stability analysis is performed in terms of an effective propagation speed of varicose waves. Experiments are performed in order to test these analytical results. We measure the critical drop size at which breakup occurs, together with the decreasing effective propagation speed of varicose waves as the threshold is approached. Our theoretical predictions are in excellent agreement with the experimental measurements.

Modelling of Electromagnetic Energy Harvester with Rotational Pendulum Using Mechanical Vibrations to Scavenge Electrical Energy

A concept of non-linear electromagnetic system with the rotational magnetic pendulum for energy harvesting from mechanical vibrations was presented. The system was stimulated by vertical excitation coming from a shaker. The main assumption of the system was the montage of additional regulated stationary magnets inside coils creating double potential well, and the system was made with a 3D printing technique in order to avoid a magnetic coupling with the housing. In validation process of the system, modelling of electromagnetic effects in different configurations of magnets positions was performed with the application of a finite element method (FEM) obtaining the value of magnetic force acting on the pendulum. A laboratory measurement circuit was built and an experiment was carried out. The voltage and power outputs were measured for different excitations in range of system operational frequencies found experimentally. The experimental results of the physical system with electrical circuit and numerical estimations of the magnetic field of a stationary magnet’s configuration were used to derive a mathematical model. The equation of motion for the rotational pendulum was used to prove the broadband frequency effect.

Integration of PD-type Iterative Learning Control with Adaptive Sliding Mode Control

Proportional-Derivative type Iterative Learning Controller (PD-ILC) is combined with an Adaptive Sliding Mode Controller (ASMC) using a plug-in structure to a rotary pendulum. The ASMC adaptation law is used to update a switching gain of sliding surface in Sliding Mode Control (SMC) controller. The proposed hybrid controller stability and convergence are mathematically shown and then experimentally demonstrated using two-degree-of-freedom (2-DOF) Quanser© QUBETM Servo 2 Rotary Pendulum. Results illustrate that adaptation law helps the controllers to achieve higher accuracy tracking performance compared to the classic SMC controller. Based on the experimental results, the hybrid control of PD-ILC and ASMC has faster and more accurate tracking results than ILC controller indicating the combined controller has better performance than the individual controllers.