On the Implementation of Fuzzy VMC for an Under Actuated System

Bicakcı, Sabri

doi:10.1109/access.2019.2952294

Cited by 11 publications

(10 citation statements)

References 45 publications

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“…The controllers are designed to stabilise the mathematical model of TWR from different initial pitch angles . Moreover, the weight of matrices Q and R in this simulation are selected as Q = diag{20,1,1,5} and R = diag{10,10} following from [9]. Therefore, the linear matrix gain is obtained as ?…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Furthermore, a Linear Quadratic Regulator (LQR) was applied to the TWR system, as demonstrated in the self-balancing robot [5], walker-assisted robot [6] and inverted pendulum on a cart [7]. Fuzzy logic control is another controller utilised on the TWR as introduced in the inverted pendulum on a rail [8], [9] and rotary inverted pendulum [10], which have similar system models as the TWR. However, these linear controllers [1]- [10] can only provide stabilisation of the TWR system within restricted operating ranges of pitch angles as the linearisation is applied around the equilibrium point in its upright position.…”

Section: Introductionmentioning

confidence: 99%

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Implementation of Nonlinear Optimal Control of Two-wheel Robot with Extended Kalman Filter

Kokkrathoke

2021

2021 IEEE International Conference on Automatic Control &Amp; Intelligent Systems (I2CACIS)

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This paper presents a nonlinear freezing optimal control (NFOC) technique combined with an extended Kalman filter (EKF) for stabilising a two-wheel robot (TWR). The balancing LEGO EV3 Robot is utilised as a prototype for simulation and practical implementation to test the performance of the NFOC with EKF, compared against the well-known linear optimal control, i.e., the linear quadratic regulator (LQR) and the stand-alone NFOC. The stabilisation of the TWR system when starting from various ranges of initial pitch angles with different types of controllers are investigated and discussed. The MATLAB simulation result demonstrates wider operation ranges from both nonlinear optimal controllers over the linear one when simulated with a high-performance motor. In the case of implementation, the two nonlinear methods also displayed slightly more comprehensive initial pitch angle ranges than the linear control. Significantly, the precision of state variable estimation from the EKF technique removes the signal drift problem in the gyro sensor, which is used to measure the pitch angle of the TWR. The effectiveness of the NFOC controller combined with EKF is demonstrated by results from MATLAB simulation and implementation on the LEGO TWR.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implementation of Nonlinear Optimal Control of Two-wheel Robot with Extended Kalman Filter

Kokkrathoke

2021

2021 IEEE International Conference on Automatic Control &Amp; Intelligent Systems (I2CACIS)

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“…The angular displacement of the rod is referred to as θ. The state-space representation of a linear dynamical system is given by (1) and (2).…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The adaptive systems are used to efficiently compensate the rapid dynamic variations in the plant by autonomously modifying the controller's characteristics [1]. Hence, they are immensely favored for controlling multivariable under-actuated systems, such as, self-balancing robots, rotorcrafts, and robotic manipulators, etc [2], [3]. The rotary inverted pendulum is a nonlinear and open-loop unstable system that is widely used as a benchmark to analyze the efficacy of control algorithms for under-actuated systems [4].…”

Section: Introductionmentioning

confidence: 99%

Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

Saleem

Mahmood-ul-Hasan

2020

IEEE Access

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This paper presents the development of an indirect adaptive state-feedback controller to improve the disturbance-rejection capability of under-actuated multivariable systems. The ubiquitous Linear-Quadratic-Regulator (LQR) is employed as the baseline state-feedback controller. Despite its optimality, the LQR lacks robustness against parametric uncertainties. Hence, the main contribution of this paper is to devise and retrofit the LQR with a stable online gain-adjustment mechanism that dynamically adjusts the state weighting-coefficients of LQR's quadratic cost-function via state-error dependent nonlinear-scaling functions. An original self-mutating phase-based adaptive modulation scheme is systematically formulated in this paper to self-adjust the state weighting-coefficients. The scheme employs pre-calibrated secanthyperbolic-functions whose waveforms are dynamically reconfigured online based on the variations in magnitude and polarity of state-error variables. This augmentation dynamically alters the solution of the Riccati-Equation which modifies the state-feedback gains online. The proposed adaptation flexibly manipulates the system's control effort as the response converges to or diverges from the reference. The efficacy of proposed adaptive controller is validated by conducting hardware-in-the-loop experiments to vertically stabilize the QNET 2.0 Rotary Pendulum system. As compared to the standard LQR, the proposed adaptive controller renders rapid transits in system's response with improved damping against oscillations, while maintaining its asymptotic-stability, under bounded exogenous disturbances. INDEX TERMS Hyperbolic functions, linear quadratic regulator, cost-function, rotary inverted pendulum, self-tuning control, state weighting-coefficients.

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“…. In [14], the authors developed a fuzzy based virtual model control (VMC) for stabilization of the pendulum angle under parametric uncertainty. The proposed controller is essentially divided into three steps: (a) imagine and attach virtual components to the system followed by, (b) obtain the virtual forces and torques and finally (c) feeding these values to the real system to realize the virtual forces and torques.…”

Section: Introductionmentioning

confidence: 99%

Real-Time Swing-Up Control of Non-Linear Inverted Pendulum Using Lyapunov Based Optimized Fuzzy Logic Control

et al. 2021

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This paper investigates the efficacy of an optimized fuzzy logic controller for real-time swing-up control and stabilization to a rigidly coupled twin-arm inverted pendulum system. The proposed fuzzy controller utilizes Lyapunov criteria for controller design to ensure system stability. The membership functions are further optimized based on the entropy function. The controller design is based on the black-box approach, eliminating the need for an accurate mathematical model of the system. The experimental results shows an improvement in the transient and steady-state response of the controlled system as compared to other state-of-the-art controllers. The proposed controller exhibits a small settling time of 4.0 s and reaches the stable swing-up position within 5 oscillations. Various error indices are evaluated that validates an overall improvement in the performance of the system.

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On the Implementation of Fuzzy VMC for an Under Actuated System

Cited by 11 publications

References 45 publications

Implementation of Nonlinear Optimal Control of Two-wheel Robot with Extended Kalman Filter

Implementation of Nonlinear Optimal Control of Two-wheel Robot with Extended Kalman Filter

Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

Real-Time Swing-Up Control of Non-Linear Inverted Pendulum Using Lyapunov Based Optimized Fuzzy Logic Control

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