Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

Modified grey wolf optimised adaptive super-twisting sliding mode control of rotary inverted pendulum system

This paper proposes a modified grey wolf optimiser-based adaptive super-twisting sliding mode control algorithm for the trajectory tracking and balancing of the rotary inverted pendulum system.The super-twisting sliding mode algorithm severely alleviates the chattering present in the classical sliding mode control.It provides robustness against model uncertainties and external disturbances with the knowledge of the upper bounds of the uncertainties and disturbances.The gains of the super-twisting sliding mode algorithm are selected through adaptive law.Parameters of the adaption law are tuned using a modified grey wolf optimisation algorithm,a meta-heuristic optimisation technique.Lyapunov stability analysis is carried out to analyse the overall control system stability.The performance of the proposed control algorithm is compared with two other sliding mode control strategies present in the literature,therein showing better performance of the proposed control scheme.

Computing of LQR Technique for Nonlinear System Using Local Approximation

The main idea behind the present research is to design a state-feedback controller for an underactuated nonlinear rotary inverted pendulum module by employing the linear quadratic regulator(LQR)technique using local approximation.The LQR is an excellent method for developing a controller for nonlinear systems.It provides optimal feedback to make the closed-loop system robust and stable,rejecting external disturbances.Model-based optimal controller for a nonlinear system such as a rotatory inverted pendulum has not been designed and implemented using Newton-Euler,Lagrange method,and local approximation.Therefore,implementing LQR to an underactuated nonlinear system was vital to design a stable controller.A mathematical model has been developed for the controller design by utilizing the Newton-Euler,Lagrange method.The nonlinear model has been linearized around an equilibrium point.Linear and nonlinear models have been compared to find the range in which linear and nonlinear models’behaviour is similar.MATLAB LQR function and system dynamics have been used to estimate the controller parameters.For the performance evaluation of the designed controller,Simulink has been used.Linear and nonlinear models have been simulated along with the designed controller.Simulations have been performed for the designed controller over the linear and nonlinear system under different conditions through varying system variables.The results show that the system is stable and robust enough to act against external disturbances.The controller maintains the rotary inverted pendulum in an upright position and rejects disruptions like falling under gravitational force or any external disturbance by adjusting the rotation of the horizontal link in both linear and nonlinear environments in a specific range.The controller has been practically designed and implemented.It is vivid from the results that the controller is robust enough to reject the disturbances in milliseconds and keeps the pendulum arm deflection angle to zero degrees.

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.

Design and Implementation of a State-feedback Controller Using LQR Technique

The main objective of this research is to design a state-feedback controller for the rotary inverted pendulum module utilizing the linear quadratic regulator(LQR)technique.The controller maintains the pendulum in the inverted(upright)position and is robust enough to reject external disturbance to maintain its stability.The research work involves three major contributions:mathematical modeling,simulation,and real-time implementation.To design a controller,mathematical modeling has been done by employing the NewtonEuler,Lagrange method.The resulting model was nonlinear so linearization was required,which has been done around a working point.For the estimation of the controller parameters,MATLAB LQR function has been utilized.Simulation has been performed for the designed controller and it also has been implemented and tested over the real inverted pendulum.From the results,it is vivid that the designed controller keeps the inverted pendulum in an upright position and rejects the disturbances and falling under gravitational force by adjusting the rotation of the horizontal link.

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.