scholarly journals Fractional-Order PII1/2DD1/2 Control: Theoretical Aspects and Application to a Mechatronic Axis

2021 ◽  
Vol 11 (8) ◽  
pp. 3631
Author(s):  
Luca Bruzzone ◽  
Mario Baggetta ◽  
Pietro Fanghella
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Tracking Error ◽  
Experimental Tests ◽  
Maximum Torque ◽  
Control Effort ◽  
Tuning Method ◽  
Alternative Approach ◽  
Remarkable Reduction ◽  
Distributed Order

Fractional Calculus is usually applied to control systems by means of the well-known PIlDm scheme, which adopts integral and derivative components of non-integer orders λ and µ. An alternative approach is to add equally distributed fractional-order terms to the PID scheme instead of replacing the integer-order terms (Distributed Order PID, DOPID). This work analyzes the properties of the DOPID scheme with five terms, that is the PII1/2DD1/2 (the half-integral and the half-derivative components are added to the classical PID). The frequency domain responses of the PID, PIlDm and PII1/2DD1/2 controllers are compared, then stability features of the PII1/2DD1/2 controller are discussed. A Bode plot-based tuning method for the PII1/2DD1/2 controller is proposed and then applied to the position control of a mechatronic axis. The closed-loop behaviours of PID and PII1/2DD1/2 are compared by simulation and by experimental tests. The results show that the PII1/2DD1/2 scheme with the proposed tuning criterium allows remarkable reduction in the position error with respect to the PID, with a similar control effort and maximum torque. For the considered mechatronic axis and trapezoidal speed law, the reduction in maximum tracking error is −71% and the reduction in mean tracking error is −77%, in correspondence to a limited increase in maximum torque (+5%) and in control effort (+4%).

Angular control of differential shape-memory alloy spring actuator for underactuated dynamic system

2021 ◽  
pp. 107754632110216
Author(s):  
M Banu Sundareswari ◽  
G Then Mozhi ◽  
K Dhanalakshmi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Control Effort ◽  
Control Laws ◽  
Integer Order ◽  
Two Degree Of Freedom ◽  
Outer Primary

This article dwells on two technical aspects, the design and implementation of an upgraded version of the differential shape-memory alloy–based revolute actuator/rotary actuating mechanism for stabilization and position control of a two-degree-of-freedom centrally hinged ball on beam system. The actuator is configured with differential and inclined placement of shape-memory alloy springs to provide bidirectional angular shift. The shape-memory alloy spring actuator occupies a smaller space and provides more extensive reformation with justifiable actuation force than an equally able shape-memory alloy wire. The cross or diagonal architecture of shape-memory alloy springs provides force amplification and reduces the actuator’s control effort. The shape-memory alloy spring–embodied actuator’s function is exemplified by the highly dynamic underactuated custom-designed ball balancing system. The ball position control is experimentally demonstrated by cascade control using the control laws that have been unattempted for shape-memory alloy actuated systems; the ball is positioned with linear (integer-order and fractional-order) proportional–integral–derivative controllers optimized with genetic algorithm and particle swarm optimization at the outer/primary loop. Angular control of the shape-memory alloy actuated beam is obtained with nonlinear (integer-order and fractional-order sliding mode control) control algorithms in the inner/secondary loop.

scholarly journals Joint Position Control Based on Fractional-Order PD and PI Controllers for the Arm of the Humanoid Robot TEO

2019 ◽  
Vol 16 (06) ◽  
pp. 1950042
Author(s):  
Jorge Muñoz ◽  
Concepción A. Monje ◽  
Santiago Martínez de la Casa ◽  
Carlos Balaguer
Keyword(s):  
Fractional Order ◽  
Elbow Joint ◽  
Humanoid Robot ◽  
Position Control ◽  
Joint Position ◽  
Robust Performance ◽  
Tuning Method ◽  
Control Scheme ◽  
Pi Controllers ◽  
Humanoid Arm

This paper presents a control scheme for the humanoid robot TEO’s elbow joint based on a novel tuning method for fractional-order PD and PI controllers. Due to the graphical nature of the proposed method, a few basic operations are enough to tune the controllers, offering very competitive results compared to classic methods. The experiments show a robust performance of the system to mass changes at the tip of the humanoid arm.

Adaptive Hybrid Intelligent Tracking Control for Uncertain Fractional Order Chaotic Systems

2012 ◽  
Vol 1 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Tsung-Chih Lin ◽  
Chia-Hao Kuo
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Fuzzy Controller ◽  
Tracking Error ◽  
Adaptive Fuzzy Control ◽  
Weighting Factor ◽  
Control Effort ◽  
Plant Knowledge ◽  
Control Knowledge ◽  
And Control

This paper presents an adaptive hybrid fuzzy controller to achieve prescribed tracking performance of fractional order chaotic systems. Depending on plant knowledge and control knowledge, a weighting factor can be adjusted by combining the indirect adaptive fuzzy control effort and the direct fuzzy adaptive control effort. Nonlinear fractional order chaotic response system is fully demonstrated to track the trajectory generated from fractional order chaotic drive system. The numerical results show that tracking error and control effort can be made smaller and the proposed hybrid intelligent control scheme is more flexible during the design process.

scholarly journals Experimental Assessment of Fractional-Order PDD1/2 Control of a Brushless DC Motor with Inertial Load

Actuators ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 13
Author(s):  
Luca Bruzzone ◽  
Pietro Fanghella ◽  
Mario Baggetta
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Experimental Tests ◽  
Research Area ◽  
Digital Implementation ◽  
Integer Order ◽  
Brushless Dc ◽  
Brushless Motor ◽  
Control Schemes ◽  
Derivative Term

The application of Fractional Calculus to control mechatronic devices is a promising research area. The most common approach to Fractional-Order (FO) control design is the PIλDµ scheme, which adopts integrals and derivatives of non-integer order λ and µ. A different possible approach is to add FO terms to the PID control, instead of replacing integer order terms; for example, in the PDD1/2 scheme, the half-derivative term is added to the classical PD. In the present paper, by mainly focusing on the transitory behaviour, a comparison among PD, PDµ, and PDD1/2 control schemes is carried out, with reference to a real-world mechatronic implementation: a position-controlled rotor actuated by a DC brushless motor. While using a general non-dimensional approach, the three control schemes are first compared by continuous-time simulations, and tuning criteria are outlined. Afterwards, the effects of the discrete-time digital implementation of the controllers are investigated by both simulation and experimental tests. The results show how PDD1/2 is an effective and almost cost-free solution for improving the trajectory-tracking performance in position control of mechatronic devices, with limited computational burden and, consequently, easily implementable on most commercial motion control drives.

scholarly journals Fractional-Order Control of a Micrometric Linear Axis

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Luca Bruzzone ◽  
Pietro Fanghella
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Tracking Error ◽  
Transient State ◽  
Step Response ◽  
Controlled System ◽  
Fractional Order Control ◽  
Control Scheme ◽  
Derivative Term ◽  
Pole Location

This paper discusses the application of a particular fractional-order control scheme, the PDD1/2, to the position control of a micrometric linear axis. The PDD1/2scheme derives from the classical PD scheme with the introduction of the half-derivative term. The PD and PDD1/2schemes are compared by adopting a nondimensional approach for the sake of generality. The linear model of the closed-loop system is discussed by analysing the pole location in theσ-plane. Then, different combinations of the derivative and half-derivative terms, characterized by the same settling energy in the step response, are experimentally compared in the real mechatronic application, with nonnegligible friction effects and a position set point with trapezoidal speed law. The experimental results are coherent with the nonlinear model of the controlled system and confirm that the introduction of the half-derivative term is an interesting option for reducing the tracking error in the transient state.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

scholarly journals Implementation and intelligent gain tuning feedback–based optimal torque control of a rotary parallel robot

2021 ◽  
pp. 107754632110191
Author(s):  
Farzam Tajdari ◽  
Naeim Ebrahimi Toulkani
Keyword(s):  
Real Time ◽  
Tracking Error ◽  
Parallel Robot ◽  
Torque Control ◽  
Test Bed ◽  
Linear Quadratic ◽  
Control Effort ◽  
The Real ◽  
Unknown Disturbances ◽  
Quadratic Integral

Aiming at operating optimally minimizing error of tracking and designing control effort, this study presents a novel generalizable methodology of an optimal torque control for a 6-degree-of-freedom Stewart platform with rotary actuators. In the proposed approach, a linear quadratic integral regulator with the least sensitivity to controller parameter choices is designed, associated with an online artificial neural network gain tuning. The nonlinear system is implemented in ADAMS, and the controller is formulated in MATLAB to minimize the real-time tracking error robustly. To validate the controller performance, MATLAB and ADAMS are linked together and the performance of the controller on the simulated system is validated as real time. Practically, the Stewart robot is fabricated and the proposed controller is implemented. The method is assessed by simulation experiments, exhibiting the viability of the developed methodology and highlighting an improvement of 45% averagely, from the optimum and zero-error convergence points of view. Consequently, the experiment results allow demonstrating the robustness of the controller method, in the presence of the motor torque saturation, the uncertainties, and unknown disturbances such as intrinsic properties of the real test bed.

An Equivalent-Plane Cross-Coupling Position Control for Contour-Accuracy Improvement in Three-Axis Free-Form Contour Following Tasks

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Jian-Wei Ma ◽  
De-Ning Song ◽  
Zhen-Yuan Jia ◽  
Wen-Wen Jiang ◽  
Fu-Ji Wang ◽  
...  
Keyword(s):  
Error Control ◽  
Position Control ◽  
Three Dimensional ◽  
Cross Coupling ◽  
Experimental Tests ◽  
Numerical Control ◽  
Free Form ◽  
Contouring Error ◽  
Contour Following ◽  
Better Than

To reduce the contouring errors in computer-numerical-control (CNC) contour-following tasks, the cross-coupling controller (CCC) is widely researched and used. However, most existing CCCs are well-designed for two-axis contouring and can hardly be generalized to compensate three-axis curved contour following errors. This paper proposes an equivalent-plane CCC scheme so that most of the two-axis CCCs or flexibly designed algorithms can be utilized for equal control of the three-axis contouring errors. An initial-value regeneration-based Newton method is first proposed to compute the foot point from the actual motion position to the desired contour with a high accuracy, so as to establish the equivalent plane where the estimated three-dimensional contouring-error vector is included. After that, the signed contouring error is computed in the equivalent plane, thus a typical two-axis proportional-integral-differential (PID)-based CCC is utilized for its control. Finally, the two-axis control commands generated by the typical CCC are coupled to three-axis control commands according to the geometry of the established equivalent plane. Experimental tests are conducted to verify the effectiveness of the presented method. The testing results illustrate that the proposed equivalent-plane CCC performs much better than conventional method in both error estimation and error control.

scholarly journals Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Jiacai Huang ◽  
Hongsheng Li ◽  
YangQuan Chen ◽  
Qinghong Xu
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Permanent Magnet Synchronous Motor ◽  
The State ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
State Variables ◽  
Nonlinear Load ◽  
Special Case

A new robust fractional-order sliding mode controller (FOSMC) is proposed for the position control of a permanent magnet synchronous motor (PMSM). The sliding mode controller (SMC), which is insensitive to uncertainties and load disturbances, is studied widely in the application of PMSM drive. In the existing SMC method, the sliding surface is usually designed based on the integer-order integration or differentiation of the state variables, while in this proposed robust FOSMC algorithm, the sliding surface is designed based on the fractional-order calculus of the state variables. In fact, the conventional SMC method can be seen as a special case of the proposed FOSMC method. The performance and robustness of the proposed method are analyzed and tested for nonlinear load torque disturbances, and simulation results show that the proposed algorithm is more robust and effective than the conventional SMC method.

scholarly journals Deterministic Approaches to Transient Trajectory Generation

2020 ◽  
Author(s):  
Matthew A. Cooper
Keyword(s):  
Linear Time ◽  
Tracking Error ◽  
Trajectory Generation ◽  
Deterministic Approach ◽  
Van Der Pol ◽  
Linear Time Invariant ◽  
Tuning Method ◽  
Exponential Weighting ◽  
Strongly Nonlinear System ◽  
Optimal Linear

This chapter studies a deterministic approach to transient trajectory generation and control as applied to the forced Van der Pol oscillatory system. This type of system tends towards a strongly nonlinear system, which can be considered chaotic. A classical tuning method, targeted exponential weighting, and isolated trajectory fractionalization trajectory generation methods are examined. Illustrating the given deterministic approach via the Van der Pol system highlights the potentially iterative nature of deterministic methods, and that traditional optimal linear time-invariant control techniques are unable to perform as desired whereas even an idealized nonlinear feedforward control significantly outperforms at the steady-state. It will be shown that utilizing a-priori knowledge of the system dynamics will enable the isolated trajectory fractionalization method to minimize the nonlinear transient effects due to miss-modeled or unmodeled plant dynamics, and that this benefit can be coupled with the targeted exponential weighting approach for greatly decreased trajectory tracking error on the order of a 92% reduction of the objective cost function in the presented case study based on the forced Van der Pol system.

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