Double Inverted Pendulum Research Articles

Human foot force informs balance control strategies when standing on a narrow beam.

Despite the abundance of studies on the control of standing balance, insights about the roles of biomechanics and neural control have been limited. Previous work introduced an analysis combining the direction and orientation of foot-ground forces. The "intersection point" of the lines of actions of these forces exhibited a consistent pattern across healthy, young subjects when computed for different frequency components of the center of pressure signal. To investigate the control strategy of quiet stance, we applied this intersection point analysis to experimental data of 15 healthy, young subjects balancing in tandem stance on a narrow beam and on the ground. Data from the sagittal and frontal planes were analyzed separately. The task was modeled as a double-inverted pendulum controlled by an optimal controller with torque-actuated ankle and hip joints and additive white noise. To test our prediction that the controller that minimized overall joint effort would yield the best fit across the tested conditions and planes of analyses, experimental results were compared with simulation outcomes. The controller that minimized overall effort produced the best fit in both balance conditions and planes of analyses. For some conditions, the relative penalty on the hip and ankle joints varied in a way relevant to the balance condition or to the plane of analysis. These results suggest that unimpaired quiet balance in a challenging environment can be best described by a controller that maintains minimal effort through the adjustment of relative ankle and hip joint torques. NEW & NOTEWORTHY This study explored balance control in humans during a challenging task using the novel intersection point analysis, based on foot-ground force direction and point of application. Experimental data of subjects standing on a narrow beam in tandem stance were compared with modeling results of a double-inverted pendulum. The analysis showed that individuals minimized effort by adjusting ankle and hip torques, shedding light on the interplay of biomechanics and neural control in maintaining balance.

A new hybrid learning control system for robots based on spiking neural networks

This paper presents a new hybrid learning and control method that can tune their parameters based on reinforcement learning. In the new proposed method, nonlinear controllers are considered multi-input multi-output functions and then the functions are replaced with SNNs with reinforcement learning algorithms. Dopamine-modulated spike-timing-dependent plasticity (STDP) is used for reinforcement learning and manipulating the synaptic weights between the input and output of neuronal groups (for parameter adjustment). Details of the method are presented and some case studies are done on nonlinear controllers such as Fractional Order PID (FOPID) and Feedback Linearization. The structure and the dynamic equations for learning are presented, and the proposed algorithm is tested on robots and results are compared with other works. Moreover, to demonstrate the effectiveness of SNNFOPID, we conducted rigorous testing on a variety of systems including a two-wheel mobile robot, a double inverted pendulum, and a four-link manipulator robot. The results revealed impressively low errors of 0.01 m, 0.03 rad, and 0.03 rad for each system, respectively. The method is tested on another controller named Feedback Linearization, which provides acceptable results. Results show that the new method has better performance in terms of Integral Absolute Error (IAE) and is highly useful in hardware implementation due to its low energy consumption, high speed, and accuracy. The duration necessary for achieving full and stable proficiency in the control of various robotic systems using SNNFOPD, and SNNFL on an Asus Core i5 system within Simulink’s Simscape environment is as follows:– Two-link robot manipulator with SNNFOPID: 19.85656 hours– Two-link robot manipulator with SNNFL: 0.45828 hours– Double inverted pendulum with SNNFOPID: 3.455 hours– Mobile robot with SNNFOPID: 3.71948 hours– Four-link robot manipulator with SNNFOPID: 16.6789 hours.This method can be generalized to other controllers and systems like robots.

LQR and Fuzzy-PID Control Design on Double Inverted Pendulum

Double inverted pendulum is a non-linear and unstable system. Double inverted pendulum can be stabilized in the upright position by providing control to the system. In this research we compare two types of controllers namely Linear Quadratic Regulator (LQR) and Fuzzy-PID. The objective is to determine the control strategy that provides better performance on the position of the cart and pendulum angle. We modelled the system which is then linearized and given control. From the simulation results, it is proven that LQR and Fuzzy-PID controllers have been successfully designed to stabilize the double inverted pendulum. However, when given a disturbance in the form of noise step, the LQR controller has not been able to achieve the desired reference for up to 20 seconds. In another hand, the Fuzzy-PID controller is able to achieve the desired reference after 8 seconds. Therefore, it can be concluded that the Fuzzy-PID controller when applied to the Double Inverted pendulum system has better performance than the LQR controller.

New Generation of Superattenuator for Einstein Telescope: preliminary studies

Seismic noise and local disturbances are dominant noise sources for ground-based gravitational waves detectors in the low frequency region (0.1–10 Hz) limiting their sensitivity and duty cycle. With the introduction of high-performance seismic isolation systems based on mechanical pendula, the 2nd generation laser interferometric detectors have reached the scientific goal of the first direct observation of GW signals thanks to the extension of the detection bandwidth down to 10 Hz. Now, the 3rd generation instrument era is approaching, and the Einstein telescope giant interferometer is becoming a reality with the possibility to install the detector in an underground site where seismic noise is 100 times smaller than on surface. Moreover, new available technologies as well as the experience acquired in operating advanced detectors are key points to further extend the detection bandwidth down to 2 Hz with the possibility to suspend cryogenic payload and then mitigating thermal noise too. Here, we present a preliminary study devoted to improving seismic attenuation performance of the advanced VIRGO superattenuator in the low frequency region of about five orders of magnitude. Particular care has been carried on in analyzing the possibility to improve the vertical attenuation performance with a multi-stage pendulum chain equipped with magnetic anti-springs that is hung to a double inverted pendulum in nested configuration. The feedback control requirements and possible strategies to be adopted for this last element will be presented.

Design of intelligent control for flexible linear double inverted pendulum based on particle swarm optimization algorithm

For the problem of control of flexible linear double inverted pendulum (FLDIP), considering that the method of obtaining LQR parameters through traditional manual trial-and-error is too cumbersome, and the basic particle swarm optimization algorithm has a slower convergence speed and is prone to a local optimal solution, in this paper, a control method is proposed that it can achieve autonomous optimization based on improved the particle swarm optimization (PSO) algorithm. Firstly, the mathematical model of the FLDIPs is given to analyse the stability of the system. Then, the PSO algorithm is improved from the perspective of dynamically adjusting inertia weights to optimize linear quadratic regulator (LQR) parameters. Finally, through simulation comparison with the LQR control effect obtained by the manual trial and error method, the feasibility of the improved PSO algorithm is verified. This method can not only improve the control performance of the system but also effectively overcome the problem of blindness in selecting Q for traditional LQR optimal control.

Online Virtual Reality Networked Control Laboratory Applied in Control Engineering Education.

Online laboratories play an important role in engineering education. This work discusses a WebVR-based virtual laboratory system. The user enters the simulated laboratory environment through a virtual reality (VR) device and interacts with the experimental equipment, similar to hands-on experiments in a physical laboratory. In addition, the proposed system allows users to design their own control algorithms and observe the effects of different control parameters to enhance their understanding of the experiment. To illustrate the features of the proposed virtual laboratory, an example is provided in this paper, which is an experiment on a double inverted pendulum system. The experimental results show that the proposed system allows users to conduct experiments in an immersive and interactive manner and provides users with a complete experimental process from principal design to experimental operation. A solution is also provided to change any virtual laboratory into a WebVR-based virtual laboratory for education and training.

Swing-up control of double-inverted pendulum systems

Swing-up control of double-inverted pendulum systems

Template-based piecewise affine regression

Abstract We study the problem of fitting a piecewise affine (PWA) function to input–output data. Our algorithm divides the input domain into finitely many regions whose shapes are specified by a user-provided template and such that the input–output data in each region are fit by an affine function within a user-provided error tolerance. We first prove that this problem is NP-hard. Then, we present a top-down algorithmic approach for solving the problem. The algorithm considers subsets of the data points in a systematic manner, trying to fit an affine function for each subset using linear regression. If regression fails on a subset, the algorithm extracts a minimal set of points from the subset (an unsatisfiable core) that is responsible for the failure. The identified core is then used to split the current subset into smaller ones. By combining this top-down scheme with a set-covering algorithm, we derive an overall approach that provides optimal PWA models for a given error tolerance, where optimality refers to minimizing the number of pieces of the PWA model. We demonstrate our approach on three numerical examples that include PWA approximations of a widely used nonlinear insulin–glucose regulation model and a double inverted pendulum with soft contacts.

Lqr-based PID controller with variable load tuned with data-driven methods for double inverted pendulum

Lqr-based PID controller with variable load tuned with data-driven methods for double inverted pendulum

Hierarchical sliding mode control and disturbance observer for the double inverted pendulum on a cart

Hierarchical sliding mode control and disturbance observer for the double inverted pendulum on a cart

Data-Based Control of Feedback Linearizable Systems

We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources of uncertainty are considered. First, the unknown linearizing input is inexactly approximated by a set of basis functions. Second, the measured output data is contaminated by additive noise. Further, we propose an approach to approximate the solution of the data-based simulation and output matching problems, and show that the difference from the true solution is bounded. Finally, the results are illustrated on an example of a fully-actuated double inverted pendulum.

Switched Energy and Neural Network-Based Approach for Swing-Up and Tracking Control of Double Inverted Pendulum

The double inverted pendulum (DIP) system is a benchmark underactuated mechanical system. The control problem of the DIP system is challenging since it not only has high nonlinearity, but also has underactuation degree equal to two. In this article, a switched energy-based swing-up and neural network (NN) controller is proposed to solve the swing-up and tracking control problem of the DIP system when the desired position is time varying. The implementation of the proposed controller can be divided into three steps. In step one, the energy-based control method is adopted to drive the first pendulum from the downward position to the neighborhood of the upright position. In step two, the sliding mode control method is adopted to stabilize the first pendulum. Meanwhile, a method combining energy-based control and “equivalent cart” is adopted to swing up the second pendulum. In step three, on the basis of approximate nonlinear output regulation theory, the NN controller is used for achieving satisfactory position tracking performance. Finally, the effectiveness of our design is verified by experimental results.

A comprehensive approach to double inverted pendulum modelling

The problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used. The investigated properties include stability of equilibrium points, a chaos of dynamics and non-minimum phase behaviour around an upper position. The presented results refer to the model of a physical (constructed) DIP system.

Optimal LQR Controller Methods for Double Inverted Pendulum System on a Cart

Most of the systems in our lives are inherently nonlinear and unstable. In control problems in the field of engineering, the aim is to define the control laws that maximize the operating efficiency of these systems under diverse security coefficients, and constraints and minimize error rates. This study aimed to model and optimally control a Double-Inverted Pendulum System on a Cart (DIPSC). A DIPSC was modeled using the Lagrange-Euler method, and classical and optimal Linear Quadratic Regulator (LQR) control methods were designed for the control of the system. The purpose of the designed controllers is to keep the arms of the double inverted pendulum on the moving cart vertically in balance and to bring the cart to the determined balance position. The critically important Q and R parameters of the LQR control technique that is one of the optimal control techniques were obtained using the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimization (GWO) algorithms. The DIPSC system was checked using classical LQR and optimal LQR methods. All obtained results are given graphically. The proposed methods are presented and analyzed in tabular form using Settling time and Mean-Square-Error (MSE) performance criteria.

Development and tests of a thrust stand with an in-situ null position adjustment and calibration method for low power plasma thrusters

A growing number of space missions use electric propulsion systems due to their higher specific impulse and greater efficiency compared to chemical propulsion systems. Because they are able to generate relatively low thrust values, conventional thrust measurement mechanisms used for chemical propulsion systems can not be used for electric propulsion systems. Thus, millinewton level thrust measurement systems are needed to be developed for measuring the low-level thrust of these types of thrusters. At the Bogazici University Space Technologies Laboratory (BUSTLab), a double inverted pendulum type thrust stand with a changeable thrust measurement range between 6 mN – 300 mN was designed, built and tested. The measurement resolution of this thrust stand can be as low as 100 μN level and it can be adjusted by changing the flexure stiffness and the mass of a counterweight. This study investigates the BUSTLab thrust measurement system and its key design points, with a particular focus on its in-situ null position adjustment and calibration process, and methods for mitigating external perturbations during thrust measurements.

Nonlinear optimal control for the rotary double inverted pendulum

AbstractThe control problem of the rotary double inverted pendulum (double Furuta pendulum) is nontrivial because of underactuation and strong nonlinearities in the associated state‐space model. The system has three degrees of freedom (one actuated and two unactuated joints) while receiving only one control input. In this article, a novel nonlinear optimal (H‐infinity) control approach is developed for the dynamic model of the rotary double inverted pendulum. First, the dynamic model of the double pendulum undergoes approximate linearization with the use of first‐order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. At a next stage a stabilizing H‐infinity feedback controller is designed. To compute the controller's feedback gains an algebraic Riccati equation has to be solved at each time‐step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. To implement state estimation‐based control without the need to measure the entire state vector of the rotary double‐pendulum the H‐infinity Kalman filter is used as a robust state observer. The nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the rotary double inverted pendulum under moderate variations of the control input.

Real Time Swinging Up and Stabilizing a Double Inverted Pendulum Using PID-LQR

Abstract This study describes a method for swinging up and stabilizing a double inverted pendulum (DIP) in real-time utilizing a PID-LQR combined control system. Firstly, a dynamic model of the double inverted pendulum system is made up and the equations of motion are constructed. The pendulum then is moved from its unstable position to a stable one using a PID-LQR controller. A comparison of the PID-LQR controller’s output and suggestions for improving system stability is presented and is suggested combined control system.

A New Optimal Design of Stable Feedback Control of Two-Wheel System Based on Reinforcement Learning

<div>The two-wheel system design is widely used in various mobile tools, such as remote-control vehicles and robots, due to its simplicity and stability. However, the specific wheel and body models in the real world can be complex, and the control accuracy of existing algorithms may not meet practical requirements. To address this issue, we propose a double inverted pendulum on mobile device (DIPM) model to improve control performances and reduce calculations. The model is based on the kinetic and potential energy of the DIPM system, known as the Euler-Lagrange equation, and is composed of three second-order nonlinear differential equations derived by specifying Lagrange. We also propose a stable feedback control method for mobile device drive systems. Our experiments compare several mainstream reinforcement learning (RL) methods, including linear quadratic regulator (LQR) and iterative linear quadratic regulator (ILQR), as well as Q-learning, SARSA, DQN (Deep Q Network), and AC. The simulation results demonstrate that the DQN and AC methods are superior to ILQR in our designed nonlinear system. In all aspects of the test, the performance of Q-learning and SARSA is comparable to that of ILQR, with some slight improvements. However, ILQR shows its advantages at 10 deg and 20 deg. In the small deflection (between 5 and 10 deg), the DQN and AC methods perform 2% better than the traditional ILQR, and in the large deflection (10–30 deg), the DQN and AC methods perform 15% better than the traditional ILQR. Overall, RL not only has the advantages of strong versatility, wide application range, and parameter customization but also greatly reduces the difficulty of control system design and human investment, making it a promising field for future research.</div>

LQR controller design for stabilization of non-linear DIP system based on ABC algorithm

Inverted pendulum systems, such as double or single, rotational or translational inverted pendulums are non-linear and unstable, which have been the most dominant approaches for control systems. The double inverted pendulum is one kind of a non-linear, unstable system, multivariable, and strong coupling with a wide range of control methods. To model these types of systems, many techniques have been proposed so that motivating researchers to come up with new innovative solutions. The Linear Quadratic Regulator (LQR) controller has been a common controller used in this field. Meanwhile, the Artificial Bee Colony (ABC) technique has become an alternative solution for employing Bee Swarm Intelligence algorithms. The research solutions of the artificial bee colony algorithm in the literature can be beneficial, however, the utilization of discovered sources of food is ineffective. Thus, in this paper, we aim to provide a double inverted pendulum system for stabilization by selecting linear quadratic regulator parameters using a bio-inspired optimization methodology of artificial bee colony and weight matrices Q and R. The results show that when the artificial bee colony algorithm is applied to a linear quadratic regulator controller, it gains the capacity to autonomously tune itself in an online process. To further demonstrate the efficiency and viability of the suggested methodology, simulations have been performed and compared to conventional linear quadratic regulator controllers. The obtained results demonstrate that employing artificial intelligence (AI) together with the proposed controller outperforms the conventional linear quadratic regulator controllers by more than 50 % in transient response and improved time response and stability performance

Applying DDPG Algorithm to Swing-Up and Balance Control for a Double Inverted Pendulum on a Cart

In this study, we apply the Deep Deterministic Policy Gradient (DDPG) algorithm in reinforcement learning to control a double inverted pendulum on a cart (DIPC)- a high order single input-multi output (SIMO) system . The simulation results demonstrate DDPG's stability and effectiveness in achieving swing-up and balance, showing its potential for tackling challenging control tasks in robotics.