A New feedback gain matrix based LQR PI Controller for Integrator time delay process

Yıl 2017, Cilt: 30 Sayı: 4, 232 - 251, 11.12.2017

Harshavardhana Reddy K , Prabhu Ramanathan

Öz

In
this paper, a Linear Quadratic Regulator (LQR) based PI controller is proposed
for the integrator plus time delay process (IPTD). In LQR PI controller design
process the selection of weight matrices ‘Q’ plays a key role in order to
minimize settling time, peak overshoot and Integral Errors. So, In order to
improve the system performance, a new feedback gain matrix is proposed for the
optimal selection of weight matrices in the controller design.  First,
the LQR PI controller is designed for First
order time delay process (FOPDT) and then
grabbed the formulas for IPTD process by assuming the state variable as zero.
The simulation results are presented to validate the proposed method by using
different IPTD process. The proposed controller is also experimentally
validated on a temperature control process. 

Anahtar Kelimeler

LQR; Skew symmetric matrix; IPTD process; Control Matrix; PI Controller; Riccati equation

Kaynakça

• [1]. Chakraborty, Sudipta, Sandip Ghosh, and Asim Kumar Naskar. "All-PD control of pure Integrating Plus Time-Delay processes with gain and phase-margin specifications." ISA transactions (2017). [2].Hamamci, Serdar Ethem, and Muhammet Koksal. "Calculation of all stabilizing fractional-order PD controllers for integrating time delay systems." Computers & Mathematics with Applications 59.5 (2010): 1621-1629. [3]. Ogunnaike BA, Ray WH. Process dynamics modeling and control. New York: Oxford University Press; 1994. p. 666–7. [4]. Wang L, Cluette WR. PID tuning controllers for integrating processes. IEEE Proc – Control Theory Appl 1997;144:385. [5]. Srividya R, Chidambaram M. Online controller tuning for integrator plus time delay processes. Process Control Qual 1997; 59:66. [6]. Padhan DG, Majhi S. Enhanced cascade control for a class of integrating processes with time delay. ISA Trans 2013;52(1):45–55. [7]. Jin Q, Liu Q. Analytical IMC-PID design in terms of performance/robustness trade-off for integrating processes: from 2-Dof to 1-Dof. J Process Control 2014;24(3):22–32. [8]. Rao AS, Chidambaram M. PI/PID controllers design for integrating and unstable systems. In: PID control in the third millennium. Springer; London; 2012. p. 75–111. [9]. Ziegler, John G, Nathaniel B. Nichols. Optimum settings for automatic controllers. Trans ASME.1942; 64.11. [10]. Kumar, DB Santosh, and R. Padma Sree. "Tuning of IMC based PID controllers for integrating systems with time delay." ISA transactions 63 (2016): 242-255. [11]. Rivera DE, Morari M, Skogested S. Internal model control for PID controller design. Ind Eng Chem Process Des Dev 1986;25:252–65. [12]. Ali, Ahmad, and Somanath Majhi. "PI/PID controller design based on IMC and percentage overshoot specification to controller setpoint change." ISA transactions 48.1 (2009): 10-15. [13]. Selvi, J. Arputha Vijaya, T. K. Radhakrishnan, and S. Sundaram. "Performance assessment of PID and IMC tuning methods for a mixing process with time delay." ISA transactions 46.3 (2007): 391-397. [14]. Wang, Qing, Changhou Lu, and Wei Pan. "IMC PID controller tuning for stable and unstable processes with time delay." Chemical Engineering Research and Design 105 (2016): 120-129. [15]. Rao, A. Seshagiri, V. S. R. Rao, and M. Chidambaram. "Direct synthesis-based controller design for integrating processes with time delay." Journal of the Franklin Institute 346.1 (2009): 38-56. [16]. Chen, Dan, and Dale E. Seborg. "PI/PID controller design based on direct synthesis and disturbance rejection." Industrial & engineering chemistry research 41.19 (2002): 4807-4822. [17]. Seshagiri Rao A, Rao VSR, Chidambaram M. Direct synthesis based controller design for integrating processes with time delay. J Frankl Inst 2009;346:38–56. [18]. Ajmeri M, Ali A. Direct synthesis based tuning of parallel control structure of integrating systems. Int J Syst Sci 2015. http://dx.doi.org/10.1080/00207721.2013.871369. [19]. Jeng, Jyh-Cheng. "A model-free direct synthesis method for PI/PID controller design based on disturbance rejection." Chemometrics and Intelligent Laboratory Systems 147 (2015): 14-29. [20]. Rao, A. Seshagiri, V. S. R. Rao, and M. Chidambaram. "Simple analytical design of modified Smith predictor with improved performance for unstable first-order plus time delay (FOPTD) processes." Industrial & engineering chemistry research 46.13 (2007): 4561-4571. [21]. Kaya, Ibrahim. "A new Smith predictor and controller for control of processes with long dead time." ISA transactions 42.1 (2003): 101-110. [22]. Padhan, Dola Gobinda, and Somanath Majhi. "Modified Smith predictor based cascade control of unstable time delay processes." ISA transactions 51.1 (2012): 95-104. [23]. Nortcliffe, Anne, and Jonathan Love. "Varying time delay Smith predictor process controller." ISA transactions 43.1 (2004): 61-71. [24]. Camacho, Oscar, and Francisco De la Cruz. "Smith predictor based-sliding mode controller for integrating processes with elevated deadtime." ISA transactions 43.2 (2004): 257-270. [25]. Wu, Ligang, and Wei Xing Zheng. "Passivity-based sliding mode control of uncertain singular time-delay systems." Automatica 45.9 (2009): 2120-2127. [26]. Zhong, Qing-Chang, and Han-Xiong Li. "2-Degree-of-Freedom Proportional− Integral− Derivative-Type Controller Incorporating the Smith Principle for Processes with Dead Time." Industrial & engineering chemistry research 41.10 (2002): 2448-2454. [27]. Wang, Dong, et al. "Discrete-time domain two-degree-of-freedom control design for integrating and unstable processes with time delay." ISA transactions 63 (2016): 121-132. [28]. Liu, Tao, Weidong Zhang, and Furong Gao. "Analytical Two-Degrees-of-Freedom (2-DOF) Decoupling Control Scheme for Multiple-Input− Multiple-Output (MIMO) Processes with Time Delays." Industrial & engineering chemistry research 46.20 (2007): 6546-6557. [29]. Visioli, Antonio. "Experimental evaluation of a time-optimal plug & control strategy." ISA transactions 46.4 (2007): 519-525. [30]. Visioli, Antonio. "Time-optimal plug & control for integrating and FOPDT processes." Journal of Process Control 13.3 (2003): 195-202. [31]. Srivastava, Saurabh, and V. S. Pandit. "A PI/PID controller for time delay systems with desired closed loop time response and guaranteed gain and phase margins." Journal of Process Control 37 (2016): 70-77. [32]. Ali A, Majhi S. PID controller tuning for integrating processes. ISA Trans 2010;49(1):70–8. [33]. Kookos, I. K., A. I. Lygeros, and K. G. Arvanitis. "On-line PI controller tuning for integrator/dead time processes." European journal of control 5.1 (1999): 19-31. [34]. Visioli, A. "Optimal tuning of PID controllers for integral and unstable processes." IEE Proceedings-Control Theory and Applications 148.2 (2001): 180-184. [35]. Padula, F., and A. Visioli. "Optimal tuning rules for proportional-integral-derivative and fractional-order proportional-integral-derivative controllers for integral and unstable processes." IET Control Theory & Applications 6.6 (2012): 776-786. [36]. Chidambaram M, Sree RP. A simple method of tuning PID controllers for integrator/dead-time processes. Comput Chem Eng 2003;27(2):211–5. [37]. Ali, Ahmad, and Somanath Majhi. "Integral criteria for optimal tuning of PI/PID controllers for integrating processes." Asian Journal of Control 13.2 (2011): 328-337. [38]. Anil, Chitturi, and Ravi Padma Sree. "Design of optimal PID controllers for integrating systems." Indian Chemical Engineer 56.3 (2014): 215-228. [39]. Anil, Ch, and R. Padma Sree. "Tuning of proportional integral derivative controllers for integrating systems using differential evolution technique." Indian Chemical Engineer 53.4 (2011): 239-260. [40]. Bingul, Zafer. "A new PID tuning technique using differential evolution for unstable and integrating processes with time delay." International Conference on Neural Information Processing. Springer Berlin Heidelberg, 2004. [41]. Kumar, Elumalai Vinodh, Ganapathy Subramanian Raaja, Jovitha Jerome. Adaptive PSO for optimal LQR tracking control of 2 DoF laboratory helicopter. Applied Soft Computing.2016; 41:77-90. [42]. Desineni Subbaram. Naidu. Optimal Control Systems.CRC press;2003. [43]. He, Jian-Bo, Qing-Guo Wang, Tong-Heng Lee. PI/PID controller tuning via LQR approach. Chem Eng Sci.2000; 55.13:2429-39. [44]. Saurabh Srivastava, Anuraag Misra, S.K. Thakur, V.S. Pandit .An optimal PID controller via LQR for standard second order plus time delay systems. ISA T.2015; 244-53.