Modeling and Control of a PWR

    System dynamics of the PWR primary system are defined by seven differential equations (for the single precursor group simplification). Consider the linearized form of these equations, with seven state variables: δ P Po , δC, δTf , δθ1, δθ2, δTC L, δTHL, and two input variables: δρex t coolant temperature going into the steam generator? Prepare a concise report summarizing your project results using the format given in the syl1 Revised and δTSG . Forthe final class project, you will develop a state-space model of the PWR primary system and implement it in MATLAB-Simulink. Use the design parameters given in Chapter 11 of Dr. Upadhyaya’s text, along with a nominal steam generator temperature of 560.8oF. Determine if the linearized system is stable or unstable; explain how you know. Calculate the initial conditions at 100% power for each of the seven state variables. Using the open-loop response (e.g., the system with no controllers), determine the response of the primary system to a perturbation in external reactivity of δρext = −40 cents inserted as a linear ramp over 20 seconds beginning at time t = 5s (shown in Figure 1). Plot all the state variables for a total simulation time of 100 seconds. Determine the open-loop response to a perturbation in the steam generator temperature of δTSG = +10oF at time t = 5s. Plot all the state variables for a total simulation time of 100 seconds. Extra CreditExtra Credit (optional) Design a PID controller to control the power produced in the core at its steady-state value by adjusting the external reactivity insertion. Test your controller under the steam generator temperature perturbation shown in Figure 2. Note that the final temperature perturbation at t = 60s is δTSG = +2 oF. Comment on the results. How well did your controller maintain the desired power level? What was the resulting control actuation? How did this affect the Extra Credit 0 5 10 15 20 25 30 35 Time (s) -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 ($) Figure 1: Linear Ramp Reactivity Insertion labus. Discuss the results from the open loop perturbations. Compare the open loop response to the two perturbations and make declarative statements about the response of reactor power and other variables to the two perturbations. Describe the developed controller, and discuss the meaning of the values for all of the gains. Discuss the efficacy of your developed controller to maintain δ P Po under perturbations of steam generator temperature (including overshoot and settling time). Your report should include the expression (symbolic matrix representation) for all elements of the A and B matrices, as well as the computed values. All MATLAB codes and Simulink models should be included as an appendix to the report. 2 Extra Credit (optional) 0 20 40 60 80 100 Time (s) -15 -10 -5 0 5 10 TSG ( oF) Figure 2: Test Steam Generator Temperature Perturbation