The place of useful learning The University of Strathclyde is a charitable body, registered in Scotland, number SC015263 EE472/EE972 Control Principles Semester 2 Project Assignment 2020/2021 Lecturers in Semester 2: Dr Hong Yue and Dr Luis Recalde-Camacho Project Teaching Assistants: Jie Bao
Cagatay Cebeci Matthew Cole Zhiwang Feng [email protected] Jennifer Morris Shangen Tian Ke Wang Project sessions: live zoom sessions (links in MyPlace) February 17, Wednesday, 9:00 am - 11:00 am (Week 5) March 3, Wednesday, 9:00 am - 11:00 am (Week 7) March 17, Wednesday, 9:00 am - 11:00 am (Week 9) Project report submission The project report should be submitted as a single pdf document, maximum 20 pages, to MyPlace by 5pm, Thursday, April 1st, 2021. Plagiarism Please read the University’s policy and guidance on plagiarism, here: http://www.strath.ac.uk/media/ps/cs/gmap/plagiarism/plagiarism_student_booklet.pdf The place of useful learning 1 The University of Strathclyde is a charitable body, registered in Scotland, number SC015263 1. Project description Figure 1. Slug catcher installation platform Slug catcher is the part of the oil platform installation where the crude oil excavated from the bottom of the sea enters the platform (Fig.1). The crude oil consists of three main components: the oil, the gas and the water. Due to physical phenomena occurring during the transportation of crude oil through the long pipes, so called “slugs” are formed. These are high concentration of gas in the pipe travelling with the oil. When a slug of gas reaches the platform, the proportion of the three components in the crude oil changes. The purpose of the slug catcher installation is to act as a buffer, to remove the water, to separate the gas from the oil and to supply this ‘cleaned’ crude oil to other plants downstream in the installation. For the purpose of this project we will consider a simplified scheme consisting of two tanks in the installation: the Slug catcher vessel and the Free-water-knock-out vessel (Fig. 2). In order to make the Slug catcher plant function effectively, the level of crude oil in both tanks has to be maintained between an upper and lower limit. The level is also used as surge capacity to ensure a continuous and constant flow of crude oil downstream to other units. Each of the tanks is equipped with a level control loop, which is a PI controller acting on a valve downstream. For the first tank the valve is a proportional one; for the second tank, it is an equal percentage valve. The process outputs to be controlled are tank levels h1 and h2, and the controller output are the valve lifts 1L and 2L . The place of useful learning 2 The University of Strathclyde is a charitable body, registered in Scotland, number SC015263 h1 D1 q12 q2 PI 1 h1REF h2 D2 PI 2 h2REF q1 Fig. 2: Schematic diagram of the two-tank system The system consists of the following components: Tanks d , 1,2 di i in out D h q q i t iD - tank area, ih - tank level, inq - inlet flow rate, outq - outlet flow rate. Valve 1 (Proportional valve) 112 1 1min 1 1min 1min 1min 1 1 with 0.02nom hq q f L f f h Valve 2 (Equal percentage valve) 2 1 2 2 2 2min 1 with 25Lnom hq q R R h 1L , 2L - valve lift (controller output u1 and u2). The place of useful learning 3 The University of Strathclyde is a charitable body, registered in Scotland, number SC015263 Valve lift constraints The valve lifts iL are subject to the following opening and varying speed constraints: d0 1, 0.1 0.1, 1,2 di i L L i t PI Controllers (controller output iu are valve lift iL ). 1( ) ( ) ( ) , 1,2i i i iREF i u s K h s h s i T s Model Parameters Table 1 Model parameters Tank minih maxih iD inomq 1 0.4m 1.6m 1.324 2m 1 2 0.2m 1.2m 2.02 2m 0.7 Note: the units used in this model are always based on meters (m) and seconds (s) Reference tank levels The reference heights for the two tanks, between 0 to 1000 seconds, are given in Table 2. Table 2 Reference heights for two tanks Tank 1 Tank 2 Time (s) 0-200 200-800 800-1000 0-400 400-600 600-1000 iREFh (m) 0.8 0.96 0.8 0.5 0.45 0.5 Inflow The flow to the first tank is a sum of a constant flow, a sinusoidal flow (slug formation) and a stochastic noise, which can be described as 1 2( ) 0.5 0.1sin ( ) 50 q t t n t where n(t) is a band-limited white noise with noise power 0.02 and sampling time 10 seconds. The place of useful learning 4 The University of Strathclyde is a charitable body, registered in Scotland, number SC015263 2. Project tasks (1) Construct the system model in Simulink (1a) Implement the two valves and plot their input-output characteristics (q vs. L) for minimum, maximum and half of tank level, h. (10%) (1b) Implement the two tanks. (5%) (1c) Implement the two PI controllers and the valve lift constraints. (10%) (1d) Link the sub-systems to construct the whole closed-loop system. (5%) (2) Tune the two PI closed-loop control systems (2a) Considering the reference signals for tank levels given in Table 2, tune the PI controllers to give satisfactory step responses. Justify your choice in PI controller design. For each tank, plot the tank level together with the reference tank level in one scope. Also plot the control signals with and without constraints on the valve lift. (25%) (2b) Discuss the interaction between the two control loops, and how it affects your tuning of the two PI controllers. (10%) (3) LQR design of the linearised system The above nonlinear system is linearised at ࢎ = . ૡ, ࢎ = . , for which the state-space model is written as ቈࢎ ሶ ࢎሶ = ቂ−. . −. ቃ ࢎ ࢎ ൨ + ቂ−. ૡ . −. ૡቃ ࡸ ࡸ ൨ Design LQR for this linearized system, show the controlled time responses in figures. (3a) Choose ۿ = ܀ = ቂ1 00 1ቃ, design LQR controller for this linearised system to minimise T T 0 1 ( ) ( ) ( ) ( ) d 2 J t t t t t x Qx u Ru . (15%) (3b) Design the pre-compensator to remove tracking error at steady state. (10%) (3c) Fixing Q, change R for different settings. Use your simulation results to discuss the effects of the weighting factors (Q, R) on control performance. (10%) 欢迎咨询51作业君
