Elektro-Hidrolik Kol Sistemi için Lyapunov Tabanlı Gözlemci Tasarımı

Year 2022, Volume: 10 Issue: 2, 773 - 787, 30.04.2022

Mithat Önder Alper Bayrak Serkan Aksoy

https://doi.org/10.29130/dubited.1000111

Abstract

Bu çalışmada, elektro-hidrolik kol sistemlerinin yük basıncını gözlemlemek için Lyapunov tabanlı bir gözlemci tasarımı önerilmiştir. Gözlemcinin kararlılığı Lyapunov tabanlı yöntem kullanılarak araştırılmıştır. Kararlılık analizinde, gözlemci hatasının keyfi olarak küçük olacak şekilde ayarlanabilen orijin civarına yakınsadığı kanıtlanmıştır. Klasik PID denetleyicisi, elektro-hidrolik kol sisteminin konumunu kontrol etmek ve sistem durumlarını sınırlı tutmak için kullanılmıştır. Önerilen gözlemcinin performansı, MATLAB Simulink programında yapılan hesaplamalı benzetimlerle değerlendirmiştir. Gözlemcinin performansı iki durumda test edilmiştir: i) gürültüsüz durum ve ii) gürültülü durum. Gürültülü durumlarda, x_2 durumuna 30 dB ek beyaz Gauss gürültüsüne maruz bırakılmıştır. Hesaplamalı benzetim sonuçları, önerilen gözlemcinin hem gürültüsüz hem de gürültülü durumlarda verimli şekilde çalıştığını göstermektedir.

Keywords

Elektro-hidrolik kol sistemi, Lyapunov tabanlı gözlemci, Yük basıncı

Lyapunov Based Observer Design for Electro-Hydraulic Arm System

Abstract

In this paper, a Lyapunov based observer design is proposed to observe the load pressure of electro-hydraulic arm systems. The stability of the observer is investigated by using the Lyapunov based method. In the stability analysis, it is proven that the observer error converge to the vicinity of origin which can be adjusted to be arbitrarily small. The classical PID controller is used to control the position of the electro-hydraulic arm system and keep the system states bounded. The performance of the designed observer is evaluated by computational simulations which are conducted in MATLAB Simulink program. The performance of the observer is tested in two cases: i) noise free case and ii) noise case. In the noisy case, the state x_2 is exposed to the 30 dB additive white Gaussian noise. The computational simulation results are given to demonstrate that the proposed observer work efficiently in both noise free and noisy cases.

Keywords

Electro-hydraulic arm system, Lyapunov based observer, Load pressure

References

• [1]Y. Chen, “Backstepping Controller Design for Electro-hydraulic Servo System with Sliding Observer,” Proceedings of the 29th Chinese Control Conference, 29-31 July, Beijing, China, pp. 391-394, 2010.
• [2]J. Yao, Z. Jiao and D. Ma, “Extended-State-Observer-Based Output Feedback Nonlinear Robust Control of Hydraulic Systems with Backstepping,” IEEE Transaction on Industrial Electronics, vol. 61, no. 11, pp. 6285-6293, 2014.
• [3]A. Chaji and S.K.H. Sani, “Observer Based Feedback Linearization Control for Electrohydraulic Servo Systems. International Congress on Technology,” Communication and Knowledge, 11-12 November, Mashhad, Iran, pp, 226-231, 2015.
• [4]J. Yao, Z. Jiao and D. Ma, “Output Feedback Nonlinear Control for Electro-hydraulic Systems. Mechatronics,” vol. 22, no. 6, pp, 766-777, 2012.
• [5]A. Monhanty and S. Gayaka, B. Yao, “An Adaptive Robust Observer for Velocity Estimation in an Electro-hydraulic System,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 12, pp. 1076-108, 2012.
• [6]S.A. Ali, A. Christe, S. Begg and N. Langlois, “Continuous Discrete Time Observer Design for State and Disturbance Estimation of Electro-hydraulic Actuator Systems,” IEEE Transaction on Industrial Electronics, vol. 63, no. 7, pp. 4314-4324, 2016.
• [7]Q. Guo, Y. Zhang, B. G. Celler and S. W. Su, “Backstepping Control of Electrohydraulic System Based on Extended-State Observer with Plant Dynamics Largely Unknown,” IEEE Transactions on Industrial Electronics, vol. 63, no. 11, pp. 6909-6920, 2016.
• [8]P. Nakkarat and S. Kuntanapreeda, “Observer-Based Backstepping Force Control of an Electrohydraulic Actuator,” Control Engineering Practice, vol. 17, no. 8, pp. 895-902, 2009.
• [9]W. Kim, D. Won and C. C. Chung, “High Gain Observer Based Nonlinear Position Control for Electro-Hydraulic Servo Systems,” Proceeding of the 2010 American Control Conference, 30 June-2 July, Baltimore, MD, USA, pp. 1140-1446, 2010.
• [10]Q. Guo, T. Yu and D. Jiang, “High-Gain Observer-Based Output Feedback Control of Single-rod Electro-hydraulic Actuator,” IET Control Theory & Applications, vol. 9, no. 16, pp. 2395-2404, 2015.
• [11]W. Shen, H. Huang and J. Wang, “Robust Backstepping Sliding Mode Controller Investigation for a Port Plate Position Servo System Based on an Extended States Observer,” Asian Journal of Control, vol. 21, no. 1, pp. 302-311, 2019.
• [12]S. Liu and B. Yao, “Sliding Mode Flow Rate Observer Design,” Proceeding of the 6th International Conference on Fluid Power Transmission and Control, 5-8 April, Huangzhou, China, pp. 1-5, 2005.
• [13]A.A. Sofiane, “Sampled Data Observer Based Inter-Sample Output Predictor for Electrohydraulic Actuators,” ISA Transaction, vol. 58, no. 1, pp. 421-433, 2015.
• [14]P. Garimella and B. Yao, “Nonlinear Adaptive Robust Observer Design for a Class of Nonlinear Systems,” Proceeding of the 2003 American Control Conference, 4-6 June, Denver, CO, USA, pp. 4391-4396, 2003.
• [15]L. Schmidt, T. O. Andersan and H. C. Pedersen, “An Approach for State Observation in Dynamical Systems Based on the Twisting Algorithm,” IEEE International Conference on Mechatronics and Automation, 4-7 August, Takamatsu, Japan, pp. 1051-1056, 2013.
• [16]Q. Zou, D. Chen and K. Wei, “Sliding Mode Based Mode Free Control of Electro-hydraulic System with Extended State Observer,” IEEE 5th Information Technology and Mechatronics Engineering Conference, 12-14 June, Chongqing, China, pp. 1637-1641, 2020.
• [17]F. Lin, K. Ou and Y. Wang, “A Position Adaptive Control Associated with High Gain Observer for Electro-Hydraulic Servo System,” Chinese Automation Congress, 6-8 November, Shanghai, China, pp. 3345-3350, 2020.
• [18]D. Won, W. Kim and M. Tomizuka, “Nonlinear Control with High Gain Extended State Observer for Position Tracking of Electro Hydraulic Systems,” IEEE/ASME Transactions on Mechatronics, vol. 25, no. 6, pp. 2610-2621, 2020.
• [19]V. Phan, C. Vo, H. Dao and K. Ahn, “Robust Fault-Tolerant Control of an Electrohydraulic Actuator with a Novel Nonlinear Unknown Input Observer,” IEEE Access, vol. 9, no. 1, 2021 pp. 30750-30760, 2021.
• [20]Q. Zou, “Extended State Observer-Based Finite Time Control of Electro-hydraulic System via Sliding Mode Technique,” Asian Journal of Control, pp. 1-17, 2021.
• [21]Q. Guo, Q. Wang, Z. Zuo, Y. Zhang, D. Jiang and Y. Shi, “Parametric Adaptive Control of Electro-hydraulic System Driving Two DOF Robotic Arm,” IEEE 56th Annual Conference on Decision and Control, 12-15 December, Melbourne, VIC, Australia, pp. 3283-3288, 2017.