Control Of Inverted Pendulum Research Articles

RETRACTED: Design of rotational inverted pendulum control based on second-order sliding mode

Rotational Inverted Pendulum is a typical nonlinear, unstable and strong coupling system. How to design a control system to restore the equilibrium state quickly and stably is a problem worth studying. High order super twisting sliding mode system has the advantages of traditional sliding mode control system. Super twisting system can elimination control chatter due to the discontinuities of control variable which contain in traditional sliding mode system. The super twisting system is designed. The saturation function replaces the sign function in the super twisting control function to improve the smoothness of the control variable. The simulation shows that this design has excellent precision. Inverted pendulum has smaller movement stroke than traditional super twisting system. Control chatter is also smaller than traditional super twisting system.

Performance Degradation Monitoring and Recovery of Vision-Based Control Systems

As an emerging need in vision-based control that is been intensively deployed in various applications, a systematic way of automatic performance recovery after system maintenance/control performance degradation is highly desired. On the one hand, vision-based control is an interdisciplinary field and the control performance of vision-based control systems is affected by not only uncertain environmental conditions but also the image processing latency, as well as the coordination of control and image processing algorithms. On the other hand, integration of image processing, control, and performance degradation recovery remains an open problem. In light of these observations, this brief deals with performance degradation monitoring and recovery with respect to the aforementioned factors. We first introduce a performance indicator by postfiltering the residual signal with the stable image representation of the feedback controller. It reveals a new interpretation of performance degradation recovery in the input- and output-recovery context. From this perspective, a real-time performance recovery approach is presented to enhance system performance over the lifetime. In the end, a vision-based inverted pendulum control system is implemented to verify the effectiveness of the proposed approach.

Real-Time Stabilization Control of a Rotary Inverted Pendulum Using LQR-Based Sliding Mode Controller

Inverted pendulum has been a benchmark system in dynamics and control theory. This system has an inherit feature of being nonlinear, unstable and underactuated. Due to which, it is widely known as a test bench to evaluate the capability and performance of emerging control algorithms. Furthermore, the inverted pendulum system is also known to resemble many real-world problems including Segway’s, humanoid robots, to name a few. The literature on inverted pendulum system reveals a wide range of controllers. The linear quadratic regulator (LQR) is one of the well-known optimal controllers; however, it lags in robustness. The sliding mode controller is known for its robustness characteristics; however, it has a problem of non-robust reachability phase. To solve the problems in both the controllers while retrieving their advantages, this paper presents the design of a hybrid controller which is a combination of LQR and sliding mode controller for the robust control of rotary inverted pendulum. This controller uses LQR as a baseline controller for optimal performance and a sliding mode controller to robustly control the system against matched uncertainties. The robustness of the proposed controller is validated on a real-time rotary inverted pendulum subjected to an input disturbance. The obtained simulation as well as experimental results show that the proposed controller performed satisfactorily with robustness to matched uncertainties. Furthermore, the problem of chattering in the controller is dealt by smoothening the control input with insignificant loss in robustness.

Swing-up stabilization control of parallel-rotating inverted pendulum by stable manifold method

Swing-up stabilization control of parallel-rotating inverted pendulum by stable manifold method

Globally Optimal Control of Nonlinear Input-Affine Systems Under Quadratic Objective Functions Based on Trajectory Database

In this paper, an approach to optimally control nonlinear input-affine systems under quadratic objective functions based on a trajectory database is proposed. In the proposed approach, the control input is calculated by solving a two-point boundary value problem of the Euler-Lagrange equation, whose initial solution is searched from the trajectory database. By a mechanism for eliminating trajectories which found to be locally optimal from the database, the proposed approach is able to obtain globally optimal solutions for problems with multiple locally optimal trajectories that are difficult to handle appropriately with existing methods. The effectiveness of the proposed approach is demonstrated through a simulation of swing-up control of one-link inverted pendulum.

Rotary Inverted Pendulum Identification for Control by Paraconsistent Neural Network

Artificial neural networks (ANNs) have been used over the last few decades to perform tasks by learning with comparisons. Fitting input-output models, system identification, control, and pattern recognition are some fields for ANN applications. However, problems involving uncertain situations could be challenging for them. The family of paraconsistent logics (PL) is a powerful tool that can deal with uncertainty and contradictory information, so getting attention from researchers for its implications and applications in artificial intelligence. This investigation describes a novel activation function reasoned on the paraconsistent annotated logic by two-value annotations (PAL2v) rules, a variation of PL, allowing the design of a new paraconsistent neural net (PNN), applied in model identification for control (I4C) of a closed-loop rotary inverted pendulum (RIP) system.

Control of the two-wheeled inverted pendulum (TWIP) robot in presence of model uncertainty and motion restriction

Purpose The purpose of this paper is to improve control performance and safety of a real two-wheeled inverted pendulum (TWIP) robot by dealing with model uncertainty and motion restriction simultaneously, which can be extended to other TWIP robotic systems. Design/methodology/approach The inequality of lumped model uncertainty boundary is derived from original TWIP dynamics. Several motion restriction conditions are derived considering zero dynamics, centripedal force, ground friction condition, posture stability, control torque limitation and so on. Sliding-mode control (SMC) and model predictive control (MPC) are separately adopted to design controllers for longitudinal and rotational motion, while taking model uncertainty into account. The reference value of the moving velocity and acceleration, delivered to the designed controller, should be restricted in a specified range, limited by motion restrictions, to keep safe. Findings The cancelation of model uncertainty commonly existing in real system can improve control performance. The motion commands play an important role in maintaining safety and reliability of TWIP, which can be ensured by the proposed motion restriction to avoid potential movement failure, such as slipping, lateral tipping over because of turning and large fluctuation of body. Originality/value An inequation of lumped model uncertainty boundary incorporating comprehensive errors and uncertainties of system is derived and elaborately calculated to determine the switching coefficients of SMC. The motion restrictions for TWIP robot moving in 3D are derived and used to impose constraints on reference trajectory to avoid possible instability or failure of movement.

Interior Point Differential Dynamic Programming

This brief introduces a novel differential dynamic programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely feasible- and infeasible-IPDDP algorithms, are developed using a primal–dual interior-point methodology, and their local quadratic convergence properties are characterized. We show that the stationary points of the algorithms are the perturbed KKT points, and thus can be moved arbitrarily close to a locally optimal solution. Being free from the burden of the active-set methods, it can handle nonlinear state and input inequality constraints without a discernible increase in its computational complexity relative to the unconstrained case. The performance of the proposed algorithms is demonstrated using numerical experiments on three different problems: control-limited inverted pendulum, car-parking, and unicycle motion control and obstacle avoidance.

Neural network implementation of controllers for multi-channel objects synthesized by polynomial method

The implementation of neural network multichannel controllers synthesized by polynomial matrix decomposition is analysed. Objects and controllers are assumed to be linear; these allow them to be described by matrix transfer functions. The transfer function of the object is converted to the right polynomial matrix inter-simple decomposition. The transfer function of the controller is sought in the form of a left polynomial matrix of inter-simple decomposition that allows leading the characteristic matrix to the form of a linear matrix polynomial equation with two matrix indeterminates. This equation is solved by leading to a matrix equation with numeric matrix indeterminates. Then the controller equation is converted to a discrete equation. The discrete sampling step is chosen small enough to allow the systems with continuous and discrete controllers have sufficiently close transient processes. The discrete controller is converted to a structure including delay elements, adder units and amplification coefficients. Then this structure is presented in the form of a set of neurons. The operation of the algorithm is illustrated by the example of the synthesis of an unstable inverted pendulum control, which includes two PID controllers. Possible increases in neuro controller performance are demonstrated. Two PID controllers are combined into one neural network in order to further optimization.

Control of Rotary Inverted Pendulum by Using On–Off Type of Cold Gas Thrusters

This article describes the control of a rotary inverted pendulum utilizing on–off-type cold gas thrusters as the actuators, which have high similarities with thruster actuated spacecrafts with slosh dynamics. The study is completed in three phases. Firstly, a Pulse Width Modulator (PWM) design method is utilized to obtain quasi-linear thrust output from the on–off-type thrusters. Then, a single axis angle controller is designed and tested on the setup along with the PWM scheme. Finally, a pendulum is connected to the other end of the platform and a rotary inverted pendulum (Furuta Pendulum) is constructed. In this way, an inherently unstable, under-actuated, on–off driven system is obtained. For the swing-up motion of the pendulum, an energy-based method is employed. Balancing of the pendulum is achieved by an observer-based state feedback controller under small angle assumption and quasi-linear outputs from the PWM driven thrusters. All of these control methodologies are realized on a real-time target machine. The pendulum is stabilized in seven seconds after five swings, which is comparable to the systems with electric motors.

Design and control of spatial inverted pendulum with two degrees of freedom

The inverted pendulum systems have inherently unstable dynamics. In order to stabilize the inverted pendulum at upright position, an actuation mechanism should generate fast-reactive motions at the pivot point of the system. This paper addressed the design and control of a spatial inverted pendulum with two degrees of freedom (DOF). The first part of the study consists of designing a novel planar two-DOF (PRRRR) actuation mechanism in order to balance the spatial inverted pendulum. The system is underactuated and has inherently extreme nonlinearity and also the restrictions on the actuators. Then, in the second part, a second-order sliding-mode and a linear quadratic Gaussian (LQG) controller have been proposed to control the pendulum within the equilibrium position. Finally the simulation results evaluated in terms of the robustness, time response and stability show that the second-order sliding-mode controller is more robust and has fast response performances in re-stabilizing the spatial inverted pendulum, while LQG controller is better in terms of keeping the system in equilibrium during the long period of time.

Development of a Fuzzy-LQR and Fuzzy-LQG stability control for a double link rotary inverted pendulum

In this paper, a Fuzzy based Linear Quadratic Regulator (FLQR) and Linear Quadratic Gaussian (FLQG) controllers are developed for stability control of a Double Link Rotary Inverted Pendulum (DLRIP) system. The aim of this work is to study dynamic performance analysis of both FLQR and FLQG controllers and to compare them with the classical LQR and LQG controllers, respectively. A dynamic mechanical simulation model of the DLRIP was obtained using both the numerically SimMechanics toolbox in MATLAB and the analytically dynamic nonlinear equations. To determine the control performance of the controllers, Settling Time (Ts), Peak Overshoot (PO), Steady-State Error (Ess), and the total Root Mean Squared Errors (RMSEs) of the joint positions are computed. Furthermore, the dynamic responses of the controllers were compared based on robustness analysis under internal and external disturbances. To show the control performance of the controllers, several simulations were conducted. Based on the comparative results, the dynamic responses of both FLQR and FLQG controllers produce much better results than the dynamic responses of the classical LQR and LQG controllers, respectively. Moreover, the robustness results indicate that the FLQR and FLQG controllers under the internal and external disturbances were effective.

Electro Pneumatic Control System for Inverted Pendulum

Abstract The paper concerns the inverted pendulum control system with using pneumatic cylinder. A mathematical model of the pendulum used to derive the LQG controller was presented. Prepared laboratory stand was presented and described in detail. The main purpose of the work was experimental researches. A number of control process tests were conducted with variable model parameters such as additional mass, injected disturbances and so on. The results were shown on the time plots of the control object states.

Stabilization and disturbance attenuation control of the gyroscopic inverted pendulum

In this study, a control moment gyroscope is used as an actuator to stabilize the inverted pendulum. A control strategy is proposed to stabilize the inverted pendulum at the upright unstable equilibrium point and to maintain the gimbal angle as small as possible. Such a problem is formulated as a constrained H∞ disturbance attenuation problem and then transformed into solving linear matrix inequalities. The performance of the proposed controller is evaluated through simulation for linear and nonlinear cases. It is shown that the proposed state-feedback control strategy effectively stabilizes the inverted pendulum.

Optimal PID control of spatial inverted pendulum with big bang–big crunch optimization

As the extension of the linear inverted pendulum ( LIP ) and planar inverted pendulum ( PIP ) , this paper proposes a novel spatial inverted pendulum ( SIP ) . The SIP is the most general inverted pendulum ( IP ) than any existing IP. The model of the SIP is presented for the first time. The SIP inherits all the characteristics of the LIP and the PIP, which is a nonlinear, unstable and underactuated system. The SIP has five degrees of motion freedom and three control forces. Thus, it is a multiple-input and multiple-output ( MIMO ) system with nonlinear dynamics. To realize the spatial trajectory tracking of the SIP, the control structure with five PID controllers will be designed. The parameter tuning of the multiple PIDs is a challenging work for the proposed SIP model. To alleviate the difficulties of the parameter tuning for the multiple PID controllers, optimal PIDs can be achieved with the help of Big Bang-Big Crunch ( BBBC ) optimization. The BBBC algorithm can successfully optimize the parameters of the multiple PID controllers with high convergence speed. The optimization performance index of the BBBC algorithm is compared with that of the particle swarm optimization ( PSO ) . Simulation results certify the rightness and effectiveness of the proposed control and optimization methods.

Research on Visual Control System of Inverted Pendulum Based on Pixel Displacement

In inverted pendulum visual servo control system (IPVSCSs), how to achieve the fast and effective measurement of the state information of the inverted pendulum is an important task. In this paper, the characteristics of the inverted pendulum are considered and a series of image processing and positioning algorithm of the pendulum are proposed. Furthermore, the inverted pendulum control system model based on the pixel displacement is established and the LQR controller is designed. Finally, the feasibility and superiority of the proposed method are verified by real-time control experiments.

Adaptive Optimal Control of Linear Periodic Systems: An Off-Policy Value Iteration Approach

This article studies the infinite-horizon adaptive optimal control of continuous-time linear periodic (CTLP) systems. A novel value iteration (VI) based off-policy adaptive dynamic programming (ADP) algorithm is proposed for a general class of CTLP systems, so that approximate optimal solutions can be obtained directly from the collected data, without the exact knowledge of system dynamics. Under mild conditions, the proofs on uniform convergence of the proposed algorithm to the optimal solutions are given for both the model-based and model-free cases. The VI-based ADP algorithm is able to find suboptimal controllers without assuming the knowledge of an initial stabilizing controller. Application to the optimal control of a triple inverted pendulum subjected to a periodically varying load demonstrates the feasibility and effectiveness of the proposed method.

Implementing homomorphic encryption based secure feedback control

This paper is about an encryption based approach to the secure implementation of feedback controllers for physical systems. Specifically, Paillier’s homomorphic encryption is used to digitally implement a class of linear dynamic controllers, which includes the commonplace static gain and PID type feedback control laws as special cases. The developed implementation is amenable to Field Programmable Gate Array (FPGA) realization. Experimental results, including timing analysis and resource usage characteristics for different encryption key lengths, are presented for the realization of an inverted pendulum controller; as this is an unstable plant, the control is necessarily fast.

Position control of spherical inverted pendulum via improved discrete-time neural network approach

Much recently, a discrete-time neural network (NN) approach from the output regulation theory was adopted to solve the position tracking problem of the spherical inverted pendulum (SIP) system. The key of this approach is to find the approximate solution of the corresponding discrete regulator equations (DREs) of the SIP system, which are composed of 10 nonlinear algebraic functional equations. However, the procedure for calculating the approximate solution of the DREs is quite tedious and is dependent on the system parameters. In this paper, an improved discrete-time NN control algorithm is proposed, which relies on the NN approximation of the feedforward function. Since the feedforward function is two-dimensional, the improved NN approach is much simpler compared with the existing NN approach. Moreover, a distinct advantage of our approach is that it allows certain robustness to the system parameters when every state is available. Simulation results demonstrate that our approach leads to much smaller tracking errors than the existing NN approach.

Modeling and Control of a Tetrahedron-Shaped Inverted Pendulum with Torque-Actuation

Abstract This paper provides a methodical procedure for the modeling and control of a tetrahedron-shaped inverted pendulum, balancing on one of its corners. The presented implementation realizes actuation by four motorized reaction wheels with high rotary inertia on the tetrahedron’s internal sides. By applying a controlled torque on the tetrahedron’s center of mass, the system can be rotated in its environment. The considered system is implemented as a real prototype, which is briefly introduced. The modeling of the tetrahedron-shaped pendulum leads to a non-linear state space model that can be used for a much greater class of inverted pendulums with arbitrary number of reaction wheels, only by changing the parameterization. Further, the non-linear model is linearized and an appropriate control concept stabilizes the system in one of its instable equilibrium positions: standing on a corner.