Control Of Pendulum Research Articles

Optimizing inverted pendulum control: Integrating neural network adaptability

This study explores the implementation and efficacy of a neural network controller for an inverted pendulum system, contrasting it with traditional state feedback control. Initially, state feedback control exhibited limitations in managing complex system dynamics. Subsequently, a neural network controller was developed, trained using datasets from both uncontrolled and refined state space models. The refined model yielded lower training loss and superior control performance. This research demonstrates the neural network controllers enhanced adaptability and precision, offering significant improvements over traditional methods in controlling dynamic systems like inverted pendulums.

Fuzzy PID control based on genetic algorithm optimization inverted pendulum system

Abstract For the first-order inverted pendulum control system, a fuzzy PID control system based on the optimization of the genetic algorithm is proposed. The traditional genetic algorithm has the problem that the difference in the fuzzy subset parameter leads to a decrease in the interpretative ability of the fuzzy system. The main problem of the current genetic algorithm is the complexity of the computation and the low efficiency. Based on this problem, this paper proposes an improved genetic algorithm, i.e., it adopts the variance operator and adaptive change of the variance index and elite retention strategy, which solves the premature and local convergence problems of the standard genetic algorithm, in order to optimize the fuzzy system. The experimental results show that the optimized genetic algorithm gives full play to the advantages of fuzzy control in terms of interpretability and robustness, and at the same time guarantees the prediction accuracy, which provides a new research idea in the field of artificial intelligence control.

The Analytical Design and Implementation of Inverted Pendulum Control System using Linear Quadratic Regulator

The Analytical Design and Implementation of Inverted Pendulum Control System using Linear Quadratic Regulator

LMI-based State Feedback Control of the Underactuated InertiaWheel Inverted Pendulum to the Unstable Upright Position

LMI-based State Feedback Control of the Underactuated InertiaWheel Inverted Pendulum to the Unstable Upright Position

Magnetic Control of a Simple Pendulum with a Moving Pivot Point

Magnetic Control of a Simple Pendulum with a Moving Pivot Point

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.

Robust-optimal control of rotary inverted pendulum control through fuzzy descriptor-based techniques

Expanding upon the well-established Takagi–Sugeno (T–S) fuzzy model, the T–S fuzzy descriptor model emerges as a robust and flexible framework. This article introduces the development of optimal and robust-optimal controllers grounded in the principles of stability control and fuzzy descriptor systems. By transforming complicated inequalities into linear matrix inequalities (LMI), we establish the essential conditions for controller construction, as delineated in theorems. To substantiate the utility of these controllers, we employ the rotary inverted pendulum as a testbed. Through diverse simulation scenarios, these controllers, rooted in fuzzy descriptor systems, demonstrate their practicality and effectiveness in ensuring the stable control of inverted pendulum systems, even in the presence of uncertainties within the model. This study highlights the adaptability and robustness of fuzzy descriptor-based controllers, paving the way for advanced control strategies in complex and uncertain environments.

Stabilization control of rotary inverted pendulum using a novel EKF-based fuzzy adaptive sliding-mode controller: design and experimental validation

This article methodically develops an improved self-regulating fuzzy-adaptive Sliding Mode Controller (SMC) that strengthens the disturbance compensation capacity of the nonlinear rotary pendulum systems while effectively attenuating the chattering content and curbing the control energy consumption. The article contributes to augmenting the SMC with online adaptation tools to achieve the said objectives. It employs the conventional Gao’s power-rate reaching law as the baseline. The scaling gain and the power rate of the said reaching law are adaptively modulated via a pre-calibrated two-input state-error-driven fuzzy nonlinear function. Additionally, the sign function in the law is also replaced with an odd-symmetric nonlinear fuzzy function to address the hard limits imposed by the former. Finally, the membership functions of the fuzzy function are self-regulated using the Extended-Kalman-Filter to improve the compensator’s adaptability in handling the system’s rapidly changing control requirements under exogenous disturbances. The aforementioned propositions are verified by performing customized and reliable hardware-in-loop experiments on the Quanser single-link rotary pendulum platform. As compared to baseline SMC law, the proposed control procedure contributes a ∼45.2%, ∼48.5%, and ∼34.8% reduction in position-regulation errors, control energy consumption, and peak overshoots, respectively. The experimental assessment validates the proposed control system’s enhanced robustness and chattering-suppression capability.

Study of Q-learning and deep Q-network learning control for a rotary inverted pendulum system

The rotary inverted pendulum system (RIPS) is an underactuated mechanical system with highly nonlinear dynamics and it is difficult to control a RIPS using the classic control models. In the last few years, reinforcement learning (RL) has become a popular nonlinear control method. RL has a powerful potential to control systems with high non-linearity and complex dynamics, such as RIPS. Nevertheless, RL control for RIPS has not been well studied and there is limited research on the development and evaluation of this control method. In this paper, RL control algorithms are developed for the swing-up and stabilization control of a single-link rotary inverted pendulum (SLRIP) and compared with classic control methods such as PID and LQR. A physical model of the SLRIP system is created using the MATLAB/Simscape Toolbox, the model is used as a dynamic simulation in MATLAB/Simulink to train the RL agents. An agent trainer system with Q-learning (QL) and deep Q-network learning (DQNL) is proposed for the data training. Furthermore, agent actions are actuating the horizontal arm of the system and states are the angles and velocities of the pendulum and the horizontal arm. The reward is computed according to the angles of the pendulum and horizontal arm. The reward is zero when the pendulum attends the upright position. The RL algorithms are used without a deep understanding of the classical controllers and are used to implement the agent. Finally, the outcome indicates the effectiveness of the QL and DQNL algorithms compared to the conventional PID and LQR controllers.

A waveform command shaping control of a double pendulum with nonzero initial conditions

AbstractIn most material handling industries, input‐ and command‐shaping techniques are extensively used to transfer objects safely. In these techniques, most of the work assumes a single‐degree‐of‐freedom system with zero initial conditions, and some of these cases are not practical. In crane systems, a crane jib cannot be positioned exactly on top of the payload at the start of transfer motion, which forces the system to start with initial angles. Furthermore, when the hook is large and/or far from the payload, the system cannot be considered a single‐degree‐of‐freedom system. Not accounting for such conditions can create unwanted oscillations at the end of the motion. In this work, a closed‐form command shaping control of a double pendulum is suggested to eliminate the residual oscillations while considering nonzero initial angles. The equation of motion is derived and then solved to find the shaper constants analytically. This shaper has a selectable maneuvering time and ensures maximum cruising velocity. Several examples are implemented numerically and experimentally to evaluate the shaper's performance. Despite the nonzero initial conditions, the results showed that the shaper can effectively eliminate all induced vibrations at the end of the maneuver.

A New Method Investigation for Robotic Inverted Pendulum Movement and Control

A New Method Investigation for Robotic Inverted Pendulum Movement and Control

Rotary Inverted Pendulum Control with Pole Placement

The inverted pendulums are multivariable and highly unstable dynamic systems. The inverted pendulum has been used to answer many modern control and control system designs because it has several problems relating to the system model of nonlinearity, difficulty, and inactivity. In this research, the main topic is the rotatory inverted pendulum. Circular path to eliminate the path that is on the pendulum that is traversed by the transversal path. In this paper, the Inverted Rotatory Pendulum is analyzed by state feedback which is adjusted by pole placement. The result of design selection in the system is very important to pay attention to the area where the pendulum will reach the point of agreement.

Improved Inverted Pendulum Control through PID and EPID Controllers

This presentation is on studies of application of combined constant rate reaching law and proportional-integral-derivative (PID) control law (EPID) for the control of inverted pendulum system. The inverted pendulum system is similar to a typical attitude control of booster rocket undergoing the takeoff process. Recent studies indicated records of higher rates of accidents in aircrafts. The records show that about half results due to malfunctions of aircraft systems and close to one-third from propulsion system malfunctions. Others are higher complexities of modern aircraft systems and in trying to reduce cost of maintenance. Therefore, the need enhanced automation, fault detection, faults isolation, faults tolerance, faults diagnosis and faults correction. Linear control techniques may not yield the desired performances in aircraft systems due to high levels of system nonlinearities. Applications of the intelligent control counterparts may not guarantee the generation of mathematical model for in-depth analysis. The major demerit of nonlinear control methods is higher requirement of computational burden making practical implementation difficult. The model of the inverted pendulum system is a linearized analytical model. The system performance of the system was observed with the EPID and PID controllers. Furthermore the effect of sudden changes such as wind, gust or other related variations on the system was also studied using step disturbance. It was a simulation studies using MATLAB/SIMULINK software. Results showed that with the EPID a near zero deviation was achieved. Whereas with PID controller was able to only maintain a deviation of about 40. Results also indicated a near zero disturbance rejection ability with the EPID, while the PID was able to only suppress the disturbance to some extent. It implies a more robust control with the EPID was achieved for aircraft/inverted pendulum control. Hence, it implies enhanced performance and with further improvement it can be used for application in this class of systems as well as similar systems. The work would help to for basic researches in aircraft/inverted pendulum control for beginners as well as experienced researchers in the field.

Reinforcement learning to achieve real-time control of triple inverted pendulum

This work uses reinforcement learning (RL) to achieve the first-ever data-driven real-time control of an actual, not simulated, triple inverted pendulum (TIP) in a model-free way. A swing-up control task for the TIP is formulated as a Markov decision process with a dense reward function, then conducted in real time by using a model-free RL approach. To increase the sample efficiency of learning, a structure-aware virtual experience replay (VER) method is proposed; it works together with an off-policy actor-critic algorithm. The VER exploits the geometrically-symmetric property of TIPs to create virtual sample trajectories from measured ones, then uses the resulting multifold augmented dataset to effectively train actor and critic networks during the learning process. These structure-infused training data serve to obtain additional information and hence increase the convergence speed of network learning. We combine the proposed VER with a state-of-the-art actor-critic algorithm, and then validate its effectiveness through numerical simulations. Notably, the inclusion of VER amplifies computational efficiency, slashing the requisite trials, training steps, and overall duration by approximately 66.67%. Finally experiments demonstrate the real-time control capability of the proposed approach on an actual TIP system.

Tikhonov-Tuned Sliding Neural Network Decoupling Control for an Inverted Pendulum

This paper introduces the concept of intelligent control using Tikhonov regularization for nonlinear coupled systems. This research is driven by the increasing demand for advanced control techniques and aims to explore the impact of Tikhonov regularization on these systems. The primary objective is to determine the optimal regularization term and its integration with other control methods to enhance intelligent control for nonlinear coupled systems. Tikhonov regularization is a technique employed to adjust neural network weights and prevent overfitting. Additionally, the incorporation of ReLU activation function in the neural network simplifies thearchitecture, avoiding issues like gradient explosion, and optimizes controller performance. Furthermore, sliding surfaces are designed to improve control system stability and robustness. The proposed Tikhonov-tuned sliding neural network (TSN) controller ensures both stability and superior system performance. The methodology emphasizes the importance of determining optimal neural network weights and regularization terms to prevent overfitting, facilitating accurate predictions in inverted pendulum control system applications. To assess the functionality and stability of TSN, this paper employs simulations and experimental implementations to control both the rotary inverted pendulum and the arm-driven inverted pendulum. The results indicate that the proposed TSN methodologies are effective and feasible.

Inverted Pendulum Control: A Comparative Study from Conventional Control to Reinforcement Learning

The rise of deep reinforcement learning in recent years has led to its usage in solving various challenging problems, such as chess and Go games. However, despite its recent success in solving highly complex problems, a question arises on whether this class of method is best employed to solve control problems in general, such as driverless cars, mobile robot control, or industrial manipulator control. This paper presents a comparative study between various classes of control algorithms and reinforcement learning in controlling an inverted pendulum system to evaluate the performance of reinforcement learning in a control problem. A test was performed to test the performance of root locus-based control, state compensator control, proportional-derivative (PD) control, and a reinforcement learning method, namely the proximal policy optimization (PPO), to control an inverted pendulum on a cart. The performances of the transient responses (such as overshoot, peak time, and settling time) and the steady-state responses (namely steady-state error and the total energy) were compared. It is found that when given a sufficient amount of training, the reinforcement learning algorithm was able to produce a comparable solution to its control algorithm counterparts despite not knowing anything about the system’s properties. Therefore, it is best used to control plants with little to no information regarding the model where testing a particular policy is easy and safe. It is also recommended for a system with a clear objective function.

Vibration control of a flexible inverted pendulum using the planned flywheel motion

Flexible inverted pendulums have found wide applications in mechanical systems, but their stability is susceptible to external disturbances. In this study, a new strategy that employs a flywheel to suppress vibration of flexible inverted pendulums is proposed. We develop the theoretical dynamic model of flexible pendulums with a flywheel by the Euler-Bernoulli beam theory, where the axial displacement of the pendulum and geometric nonlinearities are considered. An active control method based on the Bézier trajectory is proposed, where the acceleration of the flywheel is set as the input. Additionally, the equivalent damping ratio of the system including flywheel's motion is derived. The relationship between the parameters in the control equation and the suppression effect is obtained through the simulation of the equivalent damping ratio. Then, an experimental platform is built. The experimental results show that the present control strategy has good suppression effect on the vibration of the flexible inverted pendulums when selecting appropriate parameters. Meanwhile, the results of anti-disturbance test show that the present method has a certain robustness. Finally, the simulation results show that this strategy is also effective for nonlinear forced vibration under different excitation frequencies.

Research on the Deep Deterministic Policy Algorithm Based on the First-Order Inverted Pendulum

With the mature development of artificial intelligence technology, the application of intelligent control algorithms in control systems has become a trend to meet the high-performance requirements of modern society. This paper proposes a deep deterministic policy gradient (DDPG) controller design method based on deep reinforcement learning to improve system control performance. Firstly, the optimal control policy of the DDPG algorithm is derived from the Markov decision process and the Actor–Critic algorithm. Secondly, in order to avoid local optima in traditional control systems, the capacity and the settlement method of the DDPG experience pool are adjusted to absorb positive experience to accelerate convergence and to complete efficient training. In response, and to solve the overestimation of the Q value in DDPG, the overall structure of the Critic network is changed to shorten the convergence period of DDPG at low learning rates. Finally, a first-order inverted pendulum control system was constructed in a simulation environment to verify the control effectiveness of PID, DDPG, and improved DDPG. The simulation results reveal that the improved DDPG controller has a faster response to disturbances, smaller displacement, and angular displacement of the first-order inverted pendulum. The simulation further proves that the improved DDPG algorithm has better stability and convergence and stronger anti-interference ability and stability recovery. This control method provides a certain reference for the application of reinforcement learning in traditional control systems.

Comparative analysis of inverted pendulum control

Comparative analysis of inverted pendulum control

Sliding mode control architecture for stabilization and tracking control of planar inverted pendulum

Sliding mode control architecture for stabilization and tracking control of planar inverted pendulum