GRD Journals | Global Research and Development Journal for Engineering | Emerging Research and Innovations in Civil Engineering (ERICE - 2019) | February 2019
e-ISSN: 2455-5703
State Feedback Controller for LNG Storage Tank System using Pole Placement Method 1Dashrath
S. Panchal 2Devesh P. Soni 3Dipesh H. Shah 1 P.G. Scholar 2 3 Department of Civil Engineering Department of Instrumentation and Control Engineering 1,2,3 Sardar Vallabhbhai Patel Institute of Technology Vasad, India Abstract In this paper seismic control problem is discussed for an extra-large Liquefied Natural Gas (LNG) storage tank using smart baseisolation. The seismic forces are reduced by isolating LNG tank from ground through laminated isolation bearing made from natural rubber. Magneto-rheological (MR) dampers are installed to control the excessive displacement of LNG tank system. The MR dampers are commended by state feedback controller designed using pole placement method. The efficacy and effectiveness of derived control algorithm are presented and compared with uncontrolled system for past three earthquake ground motion. The simulation results showed that the state feedback control strategy is more effective in reducing the structural responses as compared to uncontrolled system. Keyword- State Feedback Control, Magneto - Rheological Damper, Pole Placement Method __________________________________________________________________________________________________
I. INTRODUCTION Our industrialized world is characterized by increase in energy demand. As the demand of energy increases, more and even larger size of LNG storage tanks is required. Recently, implementations of seismic isolation and energy dissipation systems have been extended to liquid storage tanks, especially large capacity liquefied natural gas (LNG) storage tanks, in order to improve their performance during earthquakes. The volumes of these tanks are very large and have capacities of about 160,000 m 3. The modern LNG tank as shown in Figure 1(a) consists of an inner steel tank, which contains the LNG, and an outer concrete tank that encases and protects the inner tank. Insulation is placed between the two tank walls. The LNG storage tanks are generally used in a typical LNG chain (shown in Figure 1(b)) which consists of Extraction, Transportation and Re-gasification. Natural gas is a fossil fuel composed primarily of methane (typically, at least 90%) and small quantities of nitrogen, oxygen, carbon dioxide, sulphur compounds. The liquefaction process that produces LNG removes any oxygen, carbon dioxide, sulphur compounds, and water. At atmospheric pressure natural gas liquefies for storage when temperature is approximately about -161.52°C. LNG receiving terminals and re-gasification facilities store LNG before its re-gasification for pipeline transportation.
Fig. 1 (a): Schematic View of modern LNG Tank
Fig. 1 (b): LNG Chain: Extraction, Transportation and Regasification
All rights reserved by www.grdjournals.com
151
State Feedback Controller for LNG Storage Tank System using Pole Placement Method (GRDJE / CONFERENCE / ERICE - 2019 / 032)
Several analytical and parametric studies were carried out in past to demonstrate the effectiveness of seismic isolation for earthquake resistant design of LNG storage tanks. Malhotra et. al.[2]provided the theoretical overview of a simplified seismic design procedure for cylindrical ground supported tanks considering convective(sloshing) and impulsive actions of the fluid in concrete or flexible steel tanks which are fixed to rigid foundations. Jansen et. al. [3] presented the results of a study to evaluate the performance of several recently proposed semi-active control algorithms for use with multiple MR dampers. Iemura et. al. [4] studied the behavior of cylindrical liquid storage tanks facilitated by different passive, hybrid passive and semi- active base isolation system. Jin et. al. [5] employed axis symmetric finite elements to model the LNG storage tanks. The general purpose FE analysis program was utilized to mode the LNG liquid, the inner steel tank and the outer concrete tank. Douglas et. al.[6] addressed the external hazards to above ground full containment LNG storage tanks and also dealt with seismic design with isolators. Dotoli et. al. [7] simulated the seismic behavior of an LNG tank during an earthquake. Lee k et al.[8] carried out several parametric studies for finding out the effect due to earthquake on sloshing height and overturning moment for different liquid depths of fixed and isolated base LNG Storage tanks. Bharti et. al.[9] studied the effectiveness of MR damper for seismic response mitigation of adjacent multistory buildings using Lyapunov direct approach control scheme, involving passive-off, passive-on and semi-active control strategies. Zhang et. al.[10] analyzed the seismic response of an isolated vertical, cylindrical, extra-large liquefied natural gas (LNG) tank by a Multiple Friction Pendulum System(MFPS).A simplified finite element model by Malhotra [2] and Dunkerly [1] was used to determine the usefulness of the isolation system. D.H. Shah et al.[11] presented state feedback with integral control can cope with nonlinear characteristics at all operating points. Conversely, the controller design through relay-feedback method is not able to settle at predefined time periods. D.H. Shah et al.[12] presented state feedback with integral control can cope with nonlinear characteristics at all operating points. Conversely, PID controller designed with relay-feedback method using Z-N tuning rules are not able to settle at predefined time periods without overshoots. C.A Bin Karim et al.[13] presented a dynamic model for an AC-DC integrated power system is designed based on pole placement technique to enhance power system dynamic stability. Yan Lan et al.[14] presented the designed pole placement state feedback controller for the system has shown robustness not only in simulation based experiments but also in the real time experiments on a laboratory scale set up for a pair of inverted pendulums. In all above mentioned literatures ([2]-[14]) various control strategies have been developed to control the damper forces in the presence of disturbances. The major disadvantage of the derived control algorithms are that they cannot reject the effect of matched disturbances which is applied at the input side of the system which results in the degradation of system performance. Recently, The pole-placement method is somewhat similar to the root-locus method in that we place closed-loop poles at desired locations.
II. MODELLING OF LNG TANK Figure. 2 shows the schematic diagram of simplified model of LNG storage tank. The LNG storage tank is structurally modeled into two layers. The outer portion of the tank is modeled based on Dunkerley’s [1] simplified model whereas the inner portion is modeled based on simplified model proposed by Malhotra [2].
Fig. 2: Schematic of simplified model of LNG Tank
The procedure of structural model suggested by Malhotra et al. [2] was based on the work of veletos with some modifications that included: – The higher impulsive modal mass can be combined with the first impulsive mode whereas the higher convective modal mass can be combined with the first convective mode. – Modal heights should be modified which accounts the contribution of higher modes to the base overturning moment. – Generalizing the formula for the impulsive period so that it could be applied to steel and concrete tanks of various wall thicknesses. The state space model of LNG system [1] is represented as, ẋ (t) = Ax (t) + Bu(t) (1) y(t) = Cx (t) + Du(t) (2) Where, x(t) ∈ Rn×1 is system state vector,u(t) ∈ Rm×1 is control input vector in terms of voltage, y(t) ∈ Rr×1 is system output vector, A ∈ Rn×n , B ∈ Rn×m , C ∈ Rr×n , D ∈ Rp×n are the matrices of appropriate dimensions. All rights reserved by www.grdjournals.com
152
State Feedback Controller for LNG Storage Tank System using Pole Placement Method (GRDJE / CONFERENCE / ERICE - 2019 / 032)
Where matrices are, 0 1 0 ], B = [ ], −M −1 k −M −1 C −M −1 δ −1 −1 −1 C = [−M k −M C],D = [−M δ] 100 0 0
A=[
A. Problem Statement The main objective is to design and compare the state feedback control derived using pole placement method with uncontrolled system for LNG storage tank system (1) in the presence of matched disturbances applied at the ground level.
III. DESIGN OF STATE FEEDBACK CONTROLLER FOR LNG TANK SYSTEM The concept of feed-backing all the state variables back to the input of the system through a suitable feedback matrix in the control strategy is known as state variable feedback control technique. Using this approach, the closed-loop Eigen values of the system will be specified. Thus, the aim is to design a feedback controller that will move some or all of the open loop poles of the measured system to the desired closed loop pole locations as specified.
Fig. 3: Closed-loop control system with u = -Kx
The state feedback controller for the system (1) is defined as: u = −Kx (3) This means that the control signal u is determined by an instantaneous state. Such a scheme is called state feedback. The 1 X n matrix K is called the state feedback gain matrix. Hus substituting equation (3) in (1) we have, ẋ (t) = (A − BK)x(t) (4) The solution of this equation is given by x(t) = e(A−BK)t x(0) (5) Where x (0) is the initial state caused by external disturbances.The stability and transient- response characteristics are determined by the eigenvalues of matrix A - BK. K = [0 0 … 0 1][B|AB| … |An−1 B]−1 ∅(A) (6) Equation. (6) is known as Ackermann's formula for the design of the state feedback gain matrix K.
IV. NUMERICAL STUDY In the present study, the following parameters of LNG Storage tank are taken from the paper of Zhang Ruifu et al.[12] and that of MR damper are taken from the paper of S.D. Bharti et al.[10] The LNG Storage tank is composed of outer concrete and inner steel tank. The inner steel tank has a radius r of 40 m and total height of 35 m which is fully anchored to a concrete slab. The tank is filled to a liquid height H of 33 m. The inner tank contains LNG having density ρl as 480 kg/m3. The total mass of LNG ml is 7.96×107 kg. The tank wall is made of three courses, the lower course is 25 mm thick, the middle course is 18 mm and the upper course is 12 mm thick. The total mass of the inner tank wall miw is 1.21×106 kg, and the height of its centre of gravity hiw is 14.59 m. For steel, Es is 2 ×1011 N/m2, ρ = 7.9×103 kg/m3. The total mass of the inner tank at bottom plate mit is 1.82 107 kg. The outer tank wall is made up of concrete having height L is 40 m, the medium radius of the outer tank Dc is 41m, the wall thickness of the outer tank tc is 0.9 m, the density of the concrete ρc is 2500 kg/m3, the modulus of elasticity of the concrete Ec is 3×1010 N/m2, the Poisson’s ratio of the concrete wall υc is 0.3, the dome mass md is 2.93×107 kg and the total mass of the outer tank wall mot is 2.32×107 kg. The MR damper parameters have been suitably scaled to suit the damper deformation behavior and the values of which are: α0a = 8.70 kN/m/V, γ = 496 m-2, α0b = 6.40 kN/m/V, β = 496 m-2 , c0a = 50.30 kN s/m , η = 195 sec-1, c0b = 48.70 kN s/m/V , k0 = 0.0054 kN/m, c1a = 8106.20 kN s/m, k1 = 0.0087 kN/m, c1b = 7807.90 kN s/m/V, x0 = 0.18 m, Ad = 810.50, n = 2. Based on the above parameters for LNG Storage tank as well as for the MR damper the simulation has been generated in MATLAB using
All rights reserved by www.grdjournals.com
153
State Feedback Controller for LNG Storage Tank System using Pole Placement Method (GRDJE / CONFERENCE / ERICE - 2019 / 032)
SIMULINK Tool. The results of the study are evaluated for the past three earthquake ground motion history The Gain K is computed using Pole Placement method by Ackerman’s formulae K=[158.2800 -427.0782 -0.0188 12.6423 65.5987 -17.4428 4.7608 -5.2754] through proper selection of poles J=[-1 -2 -3 -4 -5 -6 -7 -8]. The response parameters of interest for the study are: Outer tank displacement, impulsive displacement, convective displacement and outer absolute acceleration given by figure. 4 and figure. 5 the hysteresis behavior of MR damper is also studied. The peak response quantities for each earthquake are shown in Table-1. Earthquake 1940 El Centro 1980Loma Prieta 1979 Imperial Valley Control Strategy Uncontrolled Controlled Uncontrolled Controlled Uncontrolled Controlled Outer tank Displacement(m) 0.018 0.0034 0.023 0.0024 0.033 0.01 Impulsive Displacement(m) 0.068 0.0085 0.039 0.0060 0.070 0.02 Convective Displacement(m) 0.45 0.51 0.25 0.28 1.12 1.57 Isolator Displacement(m) 0.17 0.10 0.53 Outer tank Acceleration(m/s2) 6.19 0.53 8.56 0.51 12.20 0.44 Table 1: Peak Response Quantities of the Tank Evaluated Due to Earthquake Data
Fig. 4: Displacement, Acceleration history under 1940 El Centro Earthquake
All rights reserved by www.grdjournals.com
154
State Feedback Controller for LNG Storage Tank System using Pole Placement Method (GRDJE / CONFERENCE / ERICE - 2019 / 032)
Fig. 5: MR Damper Hysteresis behavior history under 1940 El Centro Earthquake
V. CONCLUSION In this paper, a state feedback controller is designed for LNG storage tank system in the presence of matched uncertainty. The control algorithm is derived using pole placement method that drives the system variables onto the switching plane at a constant rate. The stability of closed loop MIMO system is assured through Lyapunov approach. The performance of the resulting control algorithm is compared to uncontrolled system through simulation for the selected three earthquake ground motion data. It has been observed that isolation system reduces superstructure response viz. outer tank displacement, impulsive displacement, and outer tank acceleration. Further, with the installation of state feedback controller the isolation displacement reduces significantly which is crucial from design point of view. The sloshing displacement remains essentially unaffected with introduction of control system.
REFERENCES [1] Dunkerley S. (1894), “On the Whirling and Vibration of Shaft.” Philosophical Transactions of the Royal Society of London, 185: 279-360. [2] Malhotra, P.K., Wenk T., and Wieland M. (2000), “Simple Procedure for Seismic Analysis of LiquidStorage Tanks.”Structural Engineering International, [3] Jansen, M., and Dyke, J. (2000), “Semi-active Control Strategies for MR Dampers: Comparative Study.”Journal of Engineering Mechanics, ASCE, Vol.126, no.8 [4] Iemura, H., Igarashi A., and Kalantari A (2004),. “Enhancing Dynamic Performance of Liquid Storage Tanks by Semi-Active Controlled Dampers.” 13th World Conference on Earthquake Engineering, Paper No. 773. [5] Jin, B., Jeon, S., Kim, S., Kim, Y., and Chung C.( 2004),“Earthquake Response Analysis Of LNG Storage Tank By Axisymmetric Finite Element Model And Comparison To The Results Of The Simple Model.” 13th World Conference on Earthquake Engineering, Paper No. 394. [6] Douglas, H., Rotzer, J., and Maurer, H. (2005), “Hazard and Safety Investigations for LNG Tanks.” LNG Journal, pp 23-24. [7] Dotoli, R., Lisi, D., and Bardaro, D. (2007). “Sloshing Response Of LNG Storage Tank Subjected To Seismic Loading.” 6th European LS-DYNA Users’ Conference. [8] Lee, K., Kim, J., and Seo, H. (2010), “Seismic Response of LNG Storage Tank under Different Base Conditions and Liquid Height.” The International Society of Offshore and Polar Engineers (ISOPE), ISBN 978. [9] Bharti, S. D., Dumne, S. M., and Shrimali, M. K. (2010), “Seismic response analysis of adjacent buildings connected with MR dampers.” Engineering Structures 32, pp. 2122 – 2133. [10] Ruifu, Z., Dagen, W., and Xiaosong, R. (2011), “Seismic analysis of a LNG storage tank isolated by a multiple friction pendulum system.” Earthquake Engineering and Engineering Vibration, Vol.10, No.2, pp. 253-262. [11] Dipesh H. Shah, Krupa D. Narwekar, (2013)”Implementing State Feedback Controller on Three-Tank Mixing Process” Journal of Control & Instrumentation, Volume 4, Issue 3, ISSN: 2229-6972. [12] Dipesh H. Shah (2013),”Modeling and Design of State Feedback with Integral Controller for TRMS (Twin-Rotor MIMO System)”, Journal of Control & Instrumentation, Volume 4, Issue 3, ISSN: 2229-6972. [13] Chowdhury Andalib Bin Karim, Muhammad Ahsan Zamee, (2014)” Design and Analysis of Pole-Placement Controller for Dynamic Stability Improvement of VSC-HVDC based Power System” The 9th International Forum on Strategic Technology (IFOST), October 21-23, Cox’s Bazar, Bangladesh. [14] Yan Lan, Fei Minrui(2011),”Design of State-feedback Controller by Pole Placement for a Coupled Set of Inverted Pendulums”, The Tenth International Conference on Electronic Measurement & Instruments, 978-1-4244-8161-3.
All rights reserved by www.grdjournals.com
155