Rotary Double Inverted Pendulum Research Articles

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.

Linear Control Schemes for Rotary Double Inverted Pendulum

In this article, the rotary double parallel inverted pendulum (RDPIP) is researched and presented. Additionally, some linear controllers, such as PID, PID, PID-LQR cascade, are proposed, developed to control RDPIP, and the impact of those controllers on the rotary double inverted pendulum was examined. The research and simulation results are implemented in the Matlab/Simulink toolbox to prove the ability of these types of controller in balancing this model.

Control of rotary double inverted pendulum system using LQR sliding surface based sliding mode controller

This paper presents LQR sliding surface-based Sliding Mode Controller (LQR–SMC) for balancing control of a Rotary Double Inverted Pendulum (RDIP) system. It is a challenging research topic in control engineering due to its nonlinearity and instability. The RDIP system uses only a motor to control two serially connected pendulums to stand at the upright position. The sliding surface is designed based on the LQR optimal gain. Nonsingular gain matrix is obtained by using the left inverse of the input matrix in the state space form of the system dynamics. The Lyapunov stability theory is used to determine the stability of the controller. To evaluate the performance of LQR–SMC, some performance indices, including the Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE), and the Integrated Square Error (ISE), are used. System stability can be maintained by LQR–SMC under external disturbances as well as model and parameter uncertainties.

Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

The aim of this article was to determine control strategy for balance control of rotary double inverted pendulum system, which is highly nonlinear and unstable under-actuated system. The complexities involved in rotary double inverted pendulum dynamics make this system a useful engineering test bed to test and verify newly designed controllers. In this article, a constraint-based control approach titled robust generalized dynamic inversion is designed and implemented for robust stabilization of rotary double inverted pendulum system. The robust generalized dynamic inversion control is designed in two stages; in the first stage, constraint differential equations of the controlled state variables are prescribed, which encompasses the control objectives. To enforce the constraint dynamics, the equivalent control is realized by means of Moore–Penrose generalized inversion. To enhance robustness, the switching (discontinuous) control is introduced in second stage, whose design principle is based on classical sliding mode control theory. Finally, the controllers obtained in two stages are augmented to form the resultant robust generalized dynamic inversion control law. The proposed controller ensures robustness along with improved time domain performance regardless of system nonlinearities, uncertainties, and unwanted disturbances. The stability analysis is presented for guaranteeing semi-global asymptotically stable closed loop performance via Lyapunov stability criteria. Numerical simulation and experimental investigations are carried out along with comparative analysis, to demonstrate the effectiveness of robust generalized dynamic inversion control algorithm over other conventional control methods.

Stabilization of a double inverted rotary pendulum through fractional order integral control scheme

Rotary double inverted pendulum is a highly nonlinear complex system and requires a high performance controller for its control. Using gain matrix which is obtained through state feedback technique may create complexity while removing the steady-state error for all states. Incorporating an integral action can be an alternative for these errors. Therefore, a state space–based fractional order controller with fractional integral action is designed and tested on a rotary double inverted pendulum in this article. The fractional integral controller is designed based on Bode’s ideal transfer function. Two degree of freedom is considered for tuning purpose as well. The integer order controller based on the state space approach is also shown for comparison. Simulation and experimental results are presented for both controllers of this rotary double inverted pendulum system.

Control of rotary double inverted pendulum system using mixed sensitivity H∞ controller

Balancing control of a rotary double inverted pendulum system is a challenging research topic for researchers in dynamics control field because of its nonlinear, high degree-of-freedom, under actuated and unstable characteristics. The system always works under uncertainties and disturbances. Many control algorithms fail or ineffectively control the rotary double inverted pendulum system. In this article, mixed sensitivity H∞ control is proposed to balance the rotary double inverted pendulum system. The controller is proposed to ensure the robust stability and enhance the time domain performance of the system under uncertainties and disturbances. Structure of the system, dynamics model and controller synthesis are presented. For performance evaluation, the proposed mixed sensitivity H∞ controller is compared with linear quadratic regulator from both simulation and experiment on the rotary double inverted pendulum system. The results show high performance of the proposed controller on the rotary double inverted pendulum system with model uncertainties and external disturbances.

Nonlinear stabilizing control of a rotary double inverted pendulum: a modified backstepping approach

Modified backstepping control is proposed for an under-actuated rotary double inverted pendulum. The system has actuated rotary base joint with which two unactuated links are attached. The proposed control design is a three step process for de-coupled system model. In the first stage, a backstepping controller is designed for each of the active and passive joints. In the second stage, compensation is introduced in the respective control efforts to cater for uncertain terms based on Lyapunov function for each joint. Finally, the controllers obtained in the two stages are combined to form a total control law. The performance of the proposed control scheme is evaluated by convergence analysis and simulations.

Hybrid NN predictive-based LQR controller for rotary double inverted pendulum systems: an analytical study

This paper introduces a rotary double inverted pendulum (RDIP) systems. The model is derived by using Euler–Lagrange. Linear quadratic regulator (LQR) controller is applied as the main controller to stabilise the rotary double. However, LQR alone cannot control RDIP efficiently because the plant derived in linear model is not exact model of the real plant. Practically, controller design aiming to guarantee robustness has to consider these uncertainties. In this paper, neural network predictive control is proposed to improve control performance of the conventional LQR controller. Results on control techniques from computer simulation are evaluated and compared.