An anti-windup rate-varying integral control applied to electromechanical actuator

2014 ◽  
Vol 229 (4) ◽  
pp. 692-702
Author(s):  
Mohammad Reza Sabaapour ◽  
Esmaeel Khanmirza ◽  
Siamak Ghadami
Keyword(s):  
Steady State ◽  
Trajectory Tracking ◽  
Position Control ◽  
Nonlinear Modeling ◽  
External Disturbance ◽  
Error Signal ◽  
Integral Control ◽  
Electromechanical Actuator ◽  
Good Agreement ◽  
State Error

This paper introduces a novel integral-based controller to correct steady-state error as well as to improve trajectory tracking in position control of a rotary actuator. For this aim, linear and nonlinear modeling of a rotary electromechanical actuator via conventional P-D controller has been described followed by investigation of nonlinear element's effects. The model has very good agreement with experimental results. Then, for trajectory tracking improvement and especially to reduce steady-state error induced by external disturbance, different integral based controllers such as PID, PI-D, and I-PD have been considered. Moreover, the problem of integrator saturation (integral wind-up) has been solved by modified rate varying integral method. It has been showed that a PI-D controller with modified rate varying integral can best match controlling requirements, as well as having enough simplicity for analogue implementation. Also, as a new method, it was suggested that for rate-varying integral calculation, the error rate signal could be replaced by error signal. Doing so, not only former advantages were hold, but more simplicity in controller implementation was gained. Simulation results have shown the effectiveness of the proposed method.

scholarly journals Modelling and Motion Control of BLDC motor for Pan tilt Platform

2021 ◽  
Vol 16 ◽  
pp. 183-193
Author(s):  
Imran S. Sarwar
Keyword(s):  
Steady State ◽  
Motion Control ◽  
State Feedback ◽  
Design Parameters ◽  
Bldc Motor ◽  
Tabular Form ◽  
Root Locus ◽  
Integral Control ◽  
Very High ◽  
State Error

The usage of Brush-Less Direct Current (BLDC) motor has been increased in the industry especially in the field of Aerospace and electric bikes. The requirements for motion control were generated from the human eye features. The settling time and % overshoot were the desired features and design parameters. Based on desired features, values of  and ωn were found. The root-locus technique was applied to the uncompensated and compensated system, the results were not satisfactory. The % overshoot was very high, and the steady-state error was also very high. The state feedback controller was applied to the system. The % overshoot was controlled successfully but the steady-state error was still very high. To reduce the steady-state error to zero the integral control was applied. The comparison of results is presented in tabular form in the last section.

Comprehensive Nonlinear Modeling of a Pilot Operated Relief Valve

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Osama Gad
Keyword(s):  
Steady State ◽  
Coulomb Friction ◽  
Nonlinear Modeling ◽  
Critical Parameters ◽  
Relief Valve ◽  
Proposed Model ◽  
Mode Of Operation ◽  
Velocity Changes ◽  
Pressure Changes ◽  
Good Agreement

This paper is directed toward a comprehensive nonlinear modeling and simulation of the performance of a class of a pilot operated relief valves. A mathematical model is deduced to predict the performance of the valve in the steady state and transient modes of operations. The developed model takes into consideration most nonlinearities of the valve and is studied within the MATLAB-SIMULINK environment. The validity of the proposed model is assessed experimentally in the steady state and transient modes of operations. The detailed modeling has resulted in a good agreement between simulation and experimental results. During the simulation studied, it was found that, nonlinearity occurs due to three factors: the pressure changes cause nonlinear velocity changes of the flow rate, the throttling area of the valve restriction usually changes nonlinearly, and the discharge coefficient of the throttling area of the valve restriction does not remain constant. In the transient mode of operation, the simulation studied identified some critical parameters which have a significant effect on the transient response of the valve. Most of the model’s parameters can be evaluated readily by direct measurement of the valve components dimensions thought the Coulomb friction factor and bulk modulus are tuned to match the model to the measurements.

Robot torque and position control using an electrorheological actuator

1998 ◽  
Vol 212 (3) ◽  
pp. 229-238 ◽  
Author(s):  
D J Brookfield ◽  
Z B Dlodlo
Keyword(s):  
Steady State ◽  
Applied Field ◽  
Position Control ◽  
Open Loop ◽  
Settling Time ◽  
Time Varying ◽  
Control Loop ◽  
Loop Transfer Function ◽  
Non Linear ◽  
State Error

An electrorheological (ER) clutch driven from a constant speed motor provides a steady torque independent of shaft angle and can be controlled by control of the applied field. Such an actuator avoids the ‘cogging’ variation in torque observed in d.c. servo-motors and is thus well suited to robot control applications, particularly in view of the very rapid time response of ER clutches (≍ 10−3 s). However, the relationship between applied field and torque is difficult to model, being both non-linear and time varying. Whereas the non-linearity can be shown to be relatively small, the time-varying characteristic has remained a problem. In most controlled plants, a non-linear or time-varying characteristic can be mitigated by providing a closed control loop around the plant. A PID (proportional plus integral plus derivative)-based torque controller was developed and tested. This was shown to be stable with at least critical damping and to exhibit low steady state error. Design of the controller was facilitated by the identification of the open-loop transfer function of the ER actuator. The ER actuator with torque feedback was used to position a small robot link. A second PID control loop responding to the error in the link position and tuned using the standard Ziegler and Nichols method was designed and tested. A steady state error of less than 0.75 mm was achieved with a 2 per cent settling time of 2.0 s. Finally, the link position was controlled using a single-loop controller with no torque feedback and a similar steady state error achieved with a 2 per cent settling time of 1.4 s. It is argued that the ER torque actuator is ideally suited to the actuation of robot joints where precise smooth movement is required.

scholarly journals Error Signal Differential Term Feedback Enhanced Variable Step Size FxLMS Algorithm for Piezoelectric Active Vibration Control

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Weiguang Li ◽  
Wei Wang ◽  
Bin Li ◽  
Zhichun Yang
Keyword(s):  
Steady State ◽  
Convergence Rate ◽  
Active Vibration Control ◽  
Variable Step Size ◽  
Error Signal ◽  
Step Size ◽  
Fxlms Algorithm ◽  
Variable Step ◽  
Active Vibration ◽  
State Error

FxLMS (Filtered-x Least Mean Square) algorithm is widely used in the field of AVC (active vibration control) for its good convergence and strong adaptability. However, the convergence rate and steady-state error are mutually restricted for the fixed step FxLMS algorithm. Increasing step size μ to accelerate the convergence rate will result in larger steady-state error and even cause control divergence. In this paper, a new DVSFxLMS (error signal Differential term feedback Variable Step size FxLMS) algorithm is proposed by establishing nonlinear function between μ and error signal, while using differential term of the error signal as the feedback control function. Subsequently, a DVSFxLMS controller is designed to carry out the AVC simulation and experiments on cantilever beam with PSA (piezoelectric stack actuator). Simulation and experimental results show that the proposed DVSFxLMS algorithm has faster convergence rate and smaller steady-state error than the traditional FxLMS algorithm, which also has strong antinoise ability and adaptive control ability to quickly track the variable external disturbance.

Modeling and Its Error Analysis for Load-Sensing Steering System

2013 ◽  
Vol 694-697 ◽  
pp. 678-682
Author(s):  
Hai Fang Wang ◽  
Xiao Guang Ren ◽  
Yu Rong
Keyword(s):  
Steady State ◽  
Transfer Function ◽  
Input Signal ◽  
Position Control ◽  
Steering System ◽  
Force Balance ◽  
Energy Effect ◽  
Load Sensing ◽  
Hydraulic Steering ◽  
State Error

Load-sensing hydraulic steering system is universally used in wheeled machinery for good steering regulation performance and obviously saving energy effect. The load-sensing hydraulic steering system is present, and it is considered to be a mechanical and hydraulic position control system. The flow continuity equation and force balance equation of steering system is established, the transfer function of load-sensing hydraulic steering system is obtained, the system steady-state error caused by the typical input signal and load input signal on the basis of transfer function. The main parameters affecting the steady-state error are got, and it provides theoretical support for designing and improvement of load-sensing hydraulic steering system.

scholarly journals A Trapezoidal Velocity Profile Generator for Position Control Using a Feedback Strategy

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1222 ◽  
Author(s):  
Hong-Jun Heo ◽  
Yungdeug Son ◽  
Jang-Mok Kim
Keyword(s):  
Steady State ◽  
Velocity Profile ◽  
Position Control ◽  
Dynamic Range ◽  
Initial Position ◽  
Time Base ◽  
Position Controller ◽  
Basic Functions ◽  
Trapezoidal Profile ◽  
State Error

Position control is usually achieved using a position controller and a profile generator. The profile generator produces a desired position trajectory from a position reference and predefined profiles. The position controller forces the actual position to trace the generated position trajectory. A time-based profile generator is the most famous profile generator due to its capability of generating various profiles. However, time base difference in analysis and implementation causes a steady-state error. In order to remove the steady-state error, this paper proposes a novel profile generator for a trapezoidal velocity profile generation. The proposed generator is based on a cascaded P-PI position controller which is designed to trace the position reference. A dynamic range limiter is adopted to provide the acceleration and velocity restrictions which are basic functions for generating the trapezoidal profile. In spite of these restrictions, it cannot make a desired velocity profile only using the limiter because deceleration point is inaccurate. To adjust the deceleration point, a feedback compensator is designed which requires the velocity of the deceleration point. The velocity of the deceleration point is estimated from the initial position error. The compensator moves the deceleration point to the appropriate point which can generate the desired velocity profile. The proposed profile generator can remove the steady-state error, and the position response can be easily adjusted to be either overdamped or underdamped by selecting the two gains appropriately. Several experimental results are presented to verify the usefulness of the proposed generator.

scholarly journals A Robust Adaptive Trajectory Tracking Algorithm Using SMC and Machine Learning for FFSGRs with Actuator Dead Zones

2019 ◽  
Vol 9 (18) ◽  
pp. 3837 ◽  
Author(s):  
Lin Jia ◽  
Yaonan Wang ◽  
Changfan Zhang ◽  
Kaihui Zhao ◽  
Li Liu ◽  
...  
Keyword(s):  
Machine Learning ◽  
Steady State ◽  
Trajectory Tracking ◽  
Dead Zone ◽  
Lyapunov Theory ◽  
Tracking Algorithm ◽  
Convergence Time ◽  
Model Uncertainties ◽  
Friction Forces ◽  
State Error

The actuator dead zone of free-form surface grinding robots (FFSGRs) is very common in the grinding process and has a great impact on the grinding quality of a workpiece. In this paper, an improved trajectory tracking algorithm for an FFSGR with an asymmetric actuator dead zone was proposed with consideration of friction forces, model uncertainties, and external disturbances. The presented control algorithm was based on the machine learning and sliding mode control (SMC) methods. The control compensator used neural networks to estimate the actuator’s dead zone and eliminate its effects. The robust SMC compensator acted as an auxiliary controller to guarantee the system’s stability and robustness under circumstances with model uncertainties, approximation errors, and friction forces. The stability of the closed-loop system and the asymptotic convergence of tracking errors were evaluated using Lyapunov theory. The simulation results showed that the dead zone’s non-linearity can be estimated correctly, and satisfactory trajectory tracking performance can be obtained in this way, since the influences of the actuator’s dead zone were eliminated. The convergence time of the system was reduced from 1.1 to 0.8 s, and the maximum steady-state error was reduced from 0.06 to 0.015 rad. In the grinding experiment, the joint steady-state error decreased by 21%, which proves the feasibility and effectiveness of the proposed control method.

scholarly journals ENHANCEMENT OF STABILITY ON AUTONOMOUS WAYPOINT MISSION OF QUADROTOR USING LQR INTEGRATOR CONTROL

2022 ◽  
Vol 23 (1) ◽  
pp. 129-158
Author(s):  
Oktaf Agni Dhewa ◽  
Tri Kuntoro Priyambodo ◽  
Aris Nasuha ◽  
Yasir Mohd Mustofa
Keyword(s):  
Steady State ◽  
Trajectory Tracking ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
System Specification ◽  
Linear Quadratic ◽  
Environmental Disturbances ◽  
Essential Requirement ◽  
Lqr Control ◽  
State Error

The ability of the quadrotor in the waypoint trajectory tracking becomes an essential requirement in the completion of various missions nowadays. However, the magnitude of steady-state errors and multiple overshoots due to environmental disturbances leads to motion instability. These conditions make the quadrotor experience a shift and even change direction from the reference path. As a result, to minimize steady-state error and multiple overshoots, this study employs a Linear Quadratic Regulator control method with the addition of an Integrator. Comparisons between LQR without Integrator and LQR with Integrator were performed. They were implemented on a quadrotor controller to track square and zig-zag waypoint patterns. From experimental results, LQR without Integrator produce of 2 meters steady-state error and -1.04 meters undershoot average with an accuracy of 64.84 % for square pattern, along 3.19 meters steady-state error, and -1.12 meters undershoot average with an accuracy of 46.73 % for a zig-zag way. The LQR method with integrator produce of 1.06 meters steady-state error with accuracy 94.96 % without multiple-overshoot for square pattern, the 1.06 meters steady-state error, and -0.18 meters undershoot average with an accuracy of 86.49 % for the zig-zag way. The results show that the LQR control method with Integrator can minimize and improve steady-state error and multiple overshoots in quadrotor flight. The condition makes the quadrotor able to flying path waypoints with the correct system specification. ABSTRAK: Kemampuan quadrotor dalam pengesanan lintasan waypoint menjadi syarat penting dalam menyelesaikan pelbagai misi pada masa kini. Walau bagaimanapun, besarnya ralat keadaan mantap dan banyak kelebihan kerana gangguan persekitaran menyebabkan ketidakstabilan pergerakan. Keadaan ini menjadikan quadrotor mengalami pergeseran dan bahkan mengubah arah dari jalur rujukan. Oleh itu, kajian ini menggunakan kaedah kawalan Linear Quadratic Regulator dengan penambahan integrator dalam meminimumkan ralat keadaan mantap dan banyak kelebihan. Perbandingan antara LQR tanpa Integrator dan LQR dengan Integrator dilakukan. Mereka dilaksanakan pada pengawal quadrotor untuk mengesan corak titik jalan persegi dan zig-zag. Dari hasil eksperimen, LQR tanpa Integrator menghasilkan ralat keadaan mantap 2 meter dan -1.04 meter rata-rata undur tembak dengan ketepatan 64.84% untuk corak persegi, sepanjang ralat keadaan tetap 3.19 meter, dan -1.12 meter rata-rata undur bawah dengan ketepatan 46.73 % untuk cara zig-zag. Kaedah LQR dengan integrator menghasilkan ralat keadaan mantap 1.06 meter dengan ketepatan 94.96% tanpa tembakan berlebihan untuk corak segi empat sama, ralat keadaan mantap 1.06 meter, dan rata-rata undur tembak -0.18 meter dengan ketepatan 86.49% untuk zig-zag cara. Hasilnya menunjukkan bahawa kaedah kawalan LQR dengan Integrator dapat meminimumkan dan memperbaiki ralat keadaan mantap dan banyak overhoot dalam penerbangan quadrotor. Keadaan tersebut menjadikan quadrotor dapat terbang ke titik jalan dengan spesifikasi sistem yang betul.

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