Single Inverted Pendulum System Research Articles

Robust Control of An Inverted Pendulum System Based on Policy Iteration in Reinforcement Learning

This paper is primarily focused on the robust control of an inverted pendulum system based on policy iteration in reinforcement learning. First, a mathematical model of the single inverted pendulum system is established through a force analysis of the pendulum and trolley. Second, based on the theory of robust optimal control, the robust control of the uncertain linear inverted pendulum system is transformed into an optimal control problem with an appropriate performance index. Moreover, for the uncertain linear and nonlinear systems, two reinforcement-learning control algorithms are proposed using the policy iteration method. Finally, two numerical examples are provided to validate the reinforcement learning algorithms for the robust control of the inverted pendulum systems.

A third‐order sliding mode controller for nonlinear multivariable systems

AbstractThis paper proposes a third‐order sliding mode controller for nonlinear multivariable systems with uncertain parameters and subject to external disturbances. The controller achieves fast convergence rate, high tracking accuracy, and a reduced level of chattering. The stability of the controller and its global ultimately uniform convergence is proved by the Lyapunov stability theory. Simulation results on a single inverted pendulum system are given to illustrate the effectiveness of the proposed control scheme by comparing it with methods such as a second‐order supertwisting controller, a third‐order supertwisting controller, and an integral terminal third‐order sliding mode controller.

Fixed‐time non‐singular terminal sliding mode control with globally fast convergence

This paper investigates a fixed-time terminal sliding mode (TSM) control scheme of second-order non-linear uncertain systems. A globally fast fixed-time stable system is proposed, and the convergence time is established with the Lyapunov method. Then, a novel non-singular TSM utilising the proposed fixed-time stable system and an auxiliary polynomial function is constructed. Meanwhile, a fixed-time disturbance observer technique is employed to estimate the matched lumped perturbation. Globally fast fixed-time convergence of the closed-loop system is guaranteed with the phase plane analysis and Lyapunov tools, and the upper bound of the settling time independent of the initial conditions can be predefined by the controller parameters. Finally, the simulation results of a single inverted pendulum system are included to confirm the validity of the proposed methodology while comparing with some popular TSM control strategies.

Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System

This paper presents a study of optimal control design for a single-inverted pendulum (SIP) system with the multi-objective particle swarm optimization (MOPSO) algorithm. The proportional derivative (PD) control algorithm is utilized to control the system. Since the SIP system is nonlinear and the output (the pendulum angle) cannot be directly controlled (it is under-actuated), the PD control gains are not tuned with classical approaches. In this work, the MOPSO method is used to obtain the best PD gains. The use of multi-objective optimization algorithm allows the control design of the system without the need of linearization, which is not provided by using classical methods. The multi-objective optimal control design of the nonlinear system involves four design parameters (PD gains) and six objective functions (time-domain performance indices). The Hausdorff distances of consecutive Pareto sets, obtained in the MOPSO iterations, are computed to check the convergence of the MOPSO algorithm. The MOPSO algorithm finds the Pareto set and the Pareto front efficiently. Numerical simulations and experiments of the rotary inverted pendulum system are done to verify this design technique. Numerical and experimental results show that the multi-objective optimal controls offer a wide range of choices including the ones that have comparable performances to the linear quadratic regulator (LQR) control.

Fuzzy sliding-mode control with low pass filter to reduce chattering effect: an experimental validation on Quanser SRIP

Stabilization of a single rotary inverted pendulum (SRIP) system is a benchmark nonlinear control problem. Inherent instability of SRIP in upright position and the presence of modelling uncertainty pose a challenge for control engineers. Sliding-mode control (SMC) is the most widely accepted robust control technique. Various versions of SMCs to stabilize SRIP have been reported in literature. Advantages of SMC come at the cost of chattering of input, which inhibits its usage in many practical applications. Several works have been done to reduce the chattering in SMC. Application of fuzzy logic in SMC to reduce chattering has been analysed extensively in the literature. Even though implementation of fuzzy SMC (FSMC) in theory/simulations completely eliminates chattering, practical implementation of FSMC does not reduce chattering to zero. In this paper, a filtered FSMC is proposed, which filters the high frequency component in the system input. Experimental results of SMC, FSMC and a fuzzy sliding-mode controller with filter (FSMCF) are given in this paper. Results indicate that filtering the output of FSMCF reduces the chattering effect in the system without affecting the closed loop dynamics.

Modeling and PID Control of Single-Stage Inverted Pendulum System

The dynamic model is obtained based on researching the structure of single inverted pendulum system in this paper. Mathematical model of inverted pendulum that is close to the working point is deduced by linearization. A PID control algorithm is put forward by analyzing the factor of influencing inverted pendulum stability. The effectiveness of proposed algorithm is verified by simulation. This algorithm has the features of high control precision and good stability.

Research of the Inverted Pendulum System Based on the Linear Quadratic Optimal Control

As an ideal experimental method in the study of control theory, inverted pendulum system is an indispensable tool to examine the effects of control strategy. In this paper the corresponding mathematical model and the state space equation are established according to studying the working principle and balance control problem of the single stage linear inverted pendulum system. Using MATLAB solves them and gets the consequences. Finally, the linear quadratic optimal control strategy is used to design the controller of single-stage inverted pendulum system, and a simulation study is carried out. The simulation results show the effectiveness of the most sorrow regulator of the quadratic. And basic rule can be found out between the dynamic response of the inverted pendulum system and weighting matricesandin the LQR.

Anti-Windup Digital Control Design for Time-Delayed Analog Nonlinear Systems Using Approximated Scalar Sign Function

This paper describes an approximated-scalar-sign-function-based anti-windup digital control design for analog nonlinear systems subject to input constraints. As input saturation occurs, the non-smooth saturation constraint is modeled with the approximated scalar sign function which is a smooth nonlinear function. The resulting nonlinear model is further linearized at any operating point with the optimal linearization technique, and Linear Quadratic Regulator (LQR) is then applied for a state-feedback controller optimal for each operating point. As input saturation is encountered, an iterative procedure is developed to adjust control gains by systematically updating LQR weighting matrices until the inputs lie within the saturation limits. Through global digital redesign, the analog LQR controller is converted to an equivalent digital one for keeping the essential control performance, and moreover, delay compensation is taken into account during digital redesign for compensating the potential time delays in a control loop. The swing-up and stabilization control of single rotary inverted pendulum system is used to illustrate and verify the proposed method.

A Complex Overview of Modeling and Control of the Rotary Single Inverted Pendulum System

The purpose of this paper is to present an in-depth survey of the rotary single inverted pendulum system from a control engineer's point of view. The scope of the survey includes modeling and open-loop analysis of the system as well as design and verification of balancing and swing up controllers which ensure successful stabilization of the pendulum in the unstable upright equilibrium. All relevant tasks and simulation experiments are conducted using the appropriate function blocks, GUI applications and demonstration schemes from a Simulink block library developed by the authors of the paper. The library is called Inverted Pendula Modeling and Control (IPMaC) and offers comprehensive program support for modeling, simulation and control of classical (linear) and rotary inverted pendulum systems.

Research on Fuzzy Control of Inverted Pendulum in the MATLAB Environment

Inverted Pendulum is a typical system with multivariate, nonlinear system. Research on inverted pendulum can be attributed to research on nonlinear multivariate absolutely unstable system. Its control methods and ideas have an extensive usage. In this paper, a fuzzy controller is introduced to control single inverted pendulum system, and the performance characteristic of this system is also introduced. The control result of the inverted pendulum is good, the oscillation is small. Research result indicated that the control performance of fuzzy control is to select good membership function and discourse domain.

Based on Linear Quadratic Regulator Optimal Control of Single Inverted Pendulum System Co-Simulation of ADAMS and SIMULINK

In this paper, based on linear quadratic optimal control design the controller of single inverted pendulum system, using the current epidemic method of Co-simulation to play each of the strengths of two software for simulation, Through two methods of the static and dynamic to observe and analyze the quality of feedback controller the based on linear quadratic optimal control.

Intelligent Control for Self-erecting Inverted Pendulum Via Adaptive Neuro-fuzzy Inference System

A self-erecting single inverted pendulum (SESIP) is one of typical nonlinear systems. The control scheme running the SESIP consists of two main control loops. Namely, these control loops are swing-up controller and stabilization controller. A swing-up controller of an inverted pendulum system must actuate the pendulum from the stable position. While a stabilization controller must stand the pendulum in the unstable position. To deal with this system, a lot of control techniques have been used on the basis of linearized or nonlinear model. In real-time implementation, a real inverted pendulum system has state constraints and limited amplitude of input. These problems make it difficult to design a swing-up and a stabilization controller. In this paper, first, the mathematical models of cart and single inverted pendulum system are presented. Then, the Position-Velocity controller is designed to swing-up the pendulum considering physical behavior. For stabilizing the inverted pendulum, a Takagi-Sugeno fuzzy controller with Adaptive Neuro-Fuzzy Inference System (ANFIS) architecture is used to guarantee stability at unstable equilibrium position. Experimental results are given to show the effectiveness of these controllers.

Stabilization Control with L2-Gain Disturbance Attenuation for a Kind of Limit Cycle of an Inverted Pendulum System.

In this paper, we consider such a stabilization control for a single inverted pendulum system that makes the pendulum rotating cyclically. We call this a limit cycle control of the inverted pendulum system. First, a realization law of such limit cycle is derived based on the law of mechanical energy conversion. Then, a stabilization control law for the produced limit cycle is designed based on the Lyapunov stability theory. Finally, the stabilization control law is extended so as to ensure not only stability of the limit cycle but also an L2-gain disturbance attenuation in the presence of viscosity friction and modeling error. The effectiveness of the proposed control scheme is demonstrated via experimental works.

Lecture Notes: Control Design and Its Real-Time Realization

This paper discusses a method of control design and its real-time implementation. The purpose of this paper is to provide an illustration of designing and implementing a control system to practicing engineers. A single inverted pendulum system is taken as a plant for the control design, where the control objective is to stabilize the inverted pendulum. The control design procedure is presented systematically, and the method of realizing the controller is given explicitly. Control experiments are conducted, of which results are also discussed.

Swing-up control of inverted pendulum systems

SUMMARYIn Part I a technique for the swing-up control of single inverted pendulum system is presented. The requirement is to swing-up a carriage mounted pendulum system from its natural pendent position to its inverted position. It works for all carriage balancing single inverted pendulum systems as the swing-up control algorithm does not require knowledge of the system parameters. Comparison with previous swing-up controls shows that the proposed swing-up control is simpler, eaiser. more efficient, and more robust.In Part II the technique is extended to the case of the swing-up control of double inverted pendulum systems. Use is made of a novel selective partial-state feedback control law. The nonlinear, open-loop unstable, nonminimum-phase. and interactive MIMO pendulum system is actively linearised and decoupled about a neutrally stable equilibrium by the partial-state feedback control. This technique for swing-up control is not at all sensitive to uncertainties such as modelling error and sensor noise, and is both reliable and robust.