Advanced Process Control

’Advanced Process Safety, Industrial Process Control and Instrumentation’) 1 Introduction All of the tasks required in this assignment should be attempted and a written report needs to be prepared. The report, about 10 pages, should include the analysis, calculations and simulation results along with discussions and comments plus all M-files of MatLab and/or diagrams of SIMULINK produced when completing this assignment. This assignment will form up to 34% of the total mark for the whole module. The marking scheme of this assignment is based on a full mark of 100 as a result of summation of the marks allocated to all the tasks. The initial deadline for submission of a draft is Monday 12th November 2018, and the final deadline for submission of the assignment report is Monday 3rd December 2018. A brief feedback on the draft submission will be available by Monday 19th November 2018. The draft and final submissions and feedback provision will be through the Canvas site of this module. Inlet Fi h1 h2 F1 F2 Figure 1: A process of two coupled liquid storage tanks 2 Problem Description Consider a process consisting of two liquid storage tanks shown in Fig. 1. The inlet flow rate Fi is within the rage [0, 0.1] m3/s, the cross-sectional areas of the tanks are A1 = 2 1 m2 and A2 = A1/2, the outlet flow rates are Fj = cj q hj for j = 1, 2 with c1 = 0.01 m2.5 /s and c2 = c1/2. Under normal operational conditions, liquid levels are within the range [0.1, 4] m. The objective is to design a feedback control for inlet flow rate Fi so that the outlet flow rate F2 is at an arbitrarily specified constant value within [0.005, 0.01] m3/s. 3 Tasks 1. Derive a mathematical model in terms of ordinary differential equations that describes dynamics of the liquid levels of the process, and state any assumptions needed. [15 marks] 2. Determine the process equilibrium in terms of two constant liquid levels h¯ 1 and h¯ 2, with respect to an arbitrarily specified constant inlet flow rate Fi = F¯ i , and in the SIMULINK environment, simulate the process with this F¯ i and properly chosen h1(0) and h2(0). [15 marks] 3. Linearise the derived nonlinear model around the equilibrium to determine matrices A and B in the linear state equation ˙x = Ax + Bu, where x = " h˜ 1 h˜ 2 # with h˜ j = hj − h¯ j for j = 1, 2, and u = Fi − F¯ i . [10 marks] 4. Verify the stability of the system at the equilibrium based on (a) the linearised state equation (Checking A’s eigenvalues, straightforward); (b) the original nonlinear model (Using the Lyaponove theorem, difficult). (Hint: For (b), choose v = A1 C1 α 2 e 2 1 + A2 C2 e 2 2 with ej = q h¯ j − q hj for j = 1, 2, constant α > max 4 qh1 h2 = 4 q 4 0.1 = 2.52) [15 marks] 5. Through manually tuning controller’s parameters and simulating the nonlinear process in SIMULINK, examine possibilities of use of a PI control to achieve the control objective. [10 marks] 6. Based on the linearised process model and using the robust servomechanism principle, design a feedback control to achieve the control objective. [20 marks] 7. Compare and discuss performances of the controllers designed in tasks 5 and 6 when they are applied to the nonlinear process. [15 marks] 2 4 Marking scheme The mark distribution of the individual tasks has been indicated in Section Tasks. This section explains what is looked for in assessing each completed task with the maximal achievable marks for individual sub-tasks indicated. Specific marks are awarded to subtasks/sub-units of each task according to the marker’s academic judgement. The following explanations are enumerated in the same order as in Section Tasks. 1. (a) Refer to one or more first principles on which the derivation is based. (b) Outline the main steps in achieving the final form of the equations. (c) Explain meanings of the variables and physical parameters in the derived equations. (d) State any assumptions implied in the derivation of the final form of the dynamic equations. 2. (a) Choose an adequate constant inlet flow rate F¯ i and determine the process equilibrium in terms of h¯ 1 and h¯ 2. (b) Build a SIMULINK diagram of the process model derived in Task 1. (c) Simulate the process with this F¯ i and properly chosen initial liquid levels h1(0) and h2(0), and discuss the outcomes of the simulations. 3. (a) State the principle/method of linearisation. (b) Show the main steps of linearisation of the nonlinear process model developed in Task 1. (c) Specify the constant matrices of the derived linear model. 4. (a) Calculate the eigenvalues of the system based on the linearised model derived in Task 3 and comment on the stability of the system. (b) Differentiate the suggested Lyapunov function with respect to time. 3 (c) Show clearly negativity of the time-derivative of the Lyapunov function for all values of the liquid heights around the equilibrium. 5. (a) Form a feedback control loop by adding a PI controller unit to the SIMULINK diagram built in Task 2. (b) By manually tuning the PI parameters, simulate the process with PI control and comment on fulfilment of the overall control objective. 6. (a) Explain the main steps in the controller design using the robust servomechanism principle. (b) Construct the composite matrix from the matrices of the linearised model (c) Use the pole placement function in Matlab to find the feedback matrix. (d) Modify the SIMULINK diagram of the nonlinear process model built in Task 2 by adding the controller designed by the robust servomechanism principle. 7. (a) Specify a proper condition and simulate the nonlinear process model controlled respectively by the PI controller designed in Task 5 and the servomechanism controller designed in Task 6. (b) Discuss similarities and differences in performances of the process controlled by the two controllers respectively.                                                                                                                                                                                                                                            

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