Single Rotary Inverted Pendulum Research Articles

Robust and novel two degree of freedom fractional controller based on two-loop topology for inverted pendulum

A rotary single inverted pendulum (RSIP) typically represents a space booster rocket, Segway and similar systems with unstable equilibrium. This paper proposes a novel two degree of freedom (2-DOF) fractional control strategy based on 2-loop topology for RSIP system which can be extended to control the systems with unstable equilibrium. It comprises feedback and feed-forward paths. Primary controller relates the perturbation attenuation while the secondary controller is accountable for set point tracking. To tune the parameters of proposed fractional controller a simple graphical tuning method based on frequency response is used. The study will serve the outstanding experimental results for both, stabilization and trajectory tracking tasks. The study will also serve to present a comparison of the performance of the proposed controller with the 1-DOF FOPID controller and sliding mode controller (SMC) for the RSIP system. Further to confirm the usability of the proposed controller and to avoid the random perturbations sensitivity, robustness, and stability analysis through fractional root-locus and Bode-plot is investigated.

Stabilization of unstable equilibrium point of rotary inverted pendulum using fractional controller

Many studies have been conducted by researchers globally in the recent past on the control schemes to enhance the performance of rotary single inverted pendulum (RSIP). The present paper seeks to investigate into a method to stabilize a pendulum link in upright position with a focus to minimize the deviation in rotational arm. Based on the fractional calculus, the proposed control scheme consists of two loop fractional controller in order to intensify the potentiality of RSIP. To tune the parameters of proposed fractional controller a simple graphical tuning method based on frequency response is used. The same parameters will also be tuned using dynamic particle swarm optimization (dPSO). The study will also serve to present a comparison of the performance of the proposed controller with the dynamic particle swarm optimization (dPSO) based fractional controller. Back calculation anti-windup technique will also be incorporated to compensate the saturation non-linearity. Further to confirm the usability of the proposed controller and to avoid the random perturbations sensitivity and robustness is investigated.

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.

Performance Analysis and Experimental Validation of 2-DOF Fractional-Order Controller for Underactuated Rotary Inverted Pendulum

Several numbers of controllers are developed and implemented to enhance the performance of rotary single inverted pendulum (RSIP). This paper addresses a new two-degree-of-freedom (2-DOF) fractional control strategy for RSIP, which is a composition of feedback and feed-forward paths. Primary controller relates the perturbation attenuation, while the secondary controller is accountable for set point tracking. The pole placement technique is used for the design of 2-DOF proportional integral derivative (2-DOF PID) controller. In order to intensify the potentiality of 2-DOF PID controller, it is supplemented with fractional calculus. The tuning of fractional parameters is done by frequency domain analysis using the Nyquist plot. The proposed 2-DOF fractional-order PID controller is materialized on RSIP system which out turns the outstanding experimental results for both stabilization and trajectory tracking tasks. The system is investigated for stability, sensitivity and robustness, which confirms the ability of the proposed controller to reject the external random perturbations.

Designing fuzzy controllers with variable universes of discourse using input–output data

Using field data from sensors to construct a fuzzy controller based on variable universe of discourse (VUD) is an open question that is often encountered in real-world applications. The basic structure of a VUD fuzzy controller is given in this paper. To use subconscious knowledge, the input/output data from sensors, a novel method is proposed for designing a VUD fuzzy controller. Firstly, the central points of the input fuzzy sets are distributed equidistantly and those of the output fuzzy sets are regarded as undetermined parameters. Then, an improved recursive least square algorithm is presented to identify these unknown parameters, and a cut-off condition is applied to end the recursive computation. Finally, simulation examples show that the VUD fuzzy controller constructed by the identification algorithm can satisfactorily approximate original input/output data and that it can achieve a better effect on a rotary single inverted pendulum than a general fuzzy controller.

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.

Modelling of Classical and Rotary Inverted Pendulum Systems – A Generalized Approach

The purpose of this paper is to present the design and program implementation of a general procedure which yields the mathematical model for a classical or rotary inverted pendulum system with an arbitrary number of pendulum links. Lagrange equations of the second kind with an integrated Rayleigh dissipation function are employed in model design, and the energetic balance relations, derived for the base and all pendulum links in a generalized (n-link) classical and rotary inverted pendulum system, are implemented in form of symbolic MATLAB functions and a MATLAB GUI application. The validity and accuracy of motion equations generated by the application are demonstrated by evaluating the open-loop responses of simulation models of classical double and rotary single inverted pendulum.

Random Delay Compensation for Nonlinear Systems

This paper presents the digital controller design for nonlinear system with random delay. First, the delay-free nonlinear system is linearized through optimal linearization. Then, based on this optimal linear model, an analog state-feedback controller is designed via linear quadratic regulation (LQR) to achieve a satisfactory performance in the delay-free case. Lastly, an input delay compensation technique via digital redesign is applied. The resulting digital controller can maintain the essential performance of the analog counterpart in the presence of random input delay, and also possesses the features practical for implementation, like large control period and small control signal in the transient. The proposed method is verified by the simulation results on the balance control of single rotary inverted pendulum (SRIP) as well as the physical experiments.