Modelling and Process Control
Code  Completion  Credits  Range  Language 

E181096  Z,ZK  4  2P+1C 
 Lecturer:
 Karel Petera (guarantor)
 Tutor:
 Karel Petera (guarantor)
 Supervisor:
 Department of Process Engineering
 Synopsis:

Mathematical modeling, simulation and process control, specific examples of technical applications, basic principles of control, continuous and discrete system models, control elements. Computer simulation using MATLAB and SIMULINK, system responses to changes of various parameters and disturbances, system stability, analysis and optimization of model parameters with respect to the quality of control.
 Requirements:
 Syllabus of lectures:

1. Basic equations of transport phenomena: continuity equation, steadystate and unsteady balances, reaction kinetics, phase equilibrium.
2. Outflow of the tank, unsteady balance. Solution of nonlinear equations  linearization. System stability.
3. Perfectly mixed batch reactor  mathematical model. Analytical vs numerical solution. Numerical solution methods of differential equations, Euler method of the 1st order, 2nd order, RungeKutta.
4. Batch reactor with subsequent reactions (1st order). Analytical solution, numerical solution, finding optimal reaction time to get maximum of the intermediate product, nonisothermal solution.
5. Optimization  onedimensional and multidimensional, linear, nonlinear. Onedimensional optimization  golden section method to find a minimum of model function, Brent's method. Multidimensional optimization. Constrained optimization (penalty function).
6. Continuous systems  ideally mixed tank reactor, series of 3 reactors. Response to a jump at the inlet concentration, gain of the system, time constant of the process.
7. Controlling the outlet concentration of continuous stirred tank reactor. Basic types of controllers, mathematical models, properties, constants. Feedback and feedforward controllers, manipulative variable.
8. Continuous stirred tank reactor, nonisothermal reaction of 2nd order. Diagram of stationary solutions, parameter dependancy, parameter mapping method.
9. Continuous stirred tank reactor, nonisothermal 2nd order reaction  PI controller. Stability of steadystate solution  nonlinear system of equations. Ljapunov method  linearization using Taylor's expansion, Jacobi matrix, eigenvalues.
10. Evaluation of control process quality  setting controller constants. Stability degree, critical gain of controller, integral criteria using deviations.
11. Distillation column  basic balance equations, different controller configurations.
12. SIMULINK. Block algebra, block diagram of a system, basic block types, block libraries.
 Syllabus of tutorials:

1. MATLAB, basic usage. Basic matrix operations, scripts, userdefined functions. Numerical solution of equations (fzero, fsolve), plotting graphs (plot), solution of ordinary differential equations (ode45).
2. MATLAB  solution of the tank outflow problem, friction coefficient dependancy on velocity, laminar and turbulent region, dependancy on Reynolds number. Numerical solution of differential equations, response to step change at the inlet, comparing solution of linearized and original, nonlinear equations. Finding parameter values leading to oscillatory solution.
3. Perfectly mixed batch reactor  implementation of numerical method in Matlab, comparing with ode45 method, numerical stability and time step effect, implicit scheme of solving differential eqautions, stiff problems.
4. Batch reactor with subsequent reactions  nonisothermal regime, nonlinear system of differential equations, numerical solution in Matlab. Optimization the temperature regime.
5. Isothermal series of 3 ideally mixed reactors  comparing analytical and numerical solutions in Matlab.
6. Outlet concentration control at continuous stirred tank reactor, analysis of characteristic equation roots  system stability. Simulation in Matlab, imaginary roots of characteristic equation  oscillatory solution.
7. Continuous stirred tank reactor, nonisothermal, 2nd order reaction. Diagram of steadystate solution using Matlab, stability of individual points  numerical and analytical expression of Jacobi matrix and eigenvalues.
8. Continuous stirred tank reactor, nonisothermal, 2nd order reaction  PI controller, numerical solution using Matlab, sensitivity to change of controller constants, oscillatory solution, discontinuity in solution.
9. Quality of control process  finding optimal value of PI controller integration constant using Matlab.
10. Three continuous stirred tank reactors in series  optimization of controller constants using quadratic deviation, comparing values with ZieglerNichols method.
11. Distillation column  simulation in Matlab, implementing
PI controllers.
12. SIMULINK  dynamic model of continuous stirred tank reactor, adding PID controller, controller deviation, series of three reactors.
 Study Objective:

Mathematical modeling, simulation and process control, specific examples of technical applications, basic principles of control, continuous and discrete system models, control elements. Computer simulation using MATLAB and MAPLE, system responses to changes of various parameters and disturbances, system stability, analysis and optimization of model parameters with respect to the quality of control.
 Study materials:

W.L. Luyben: Process Modeling, Simulation, and Control for Chemical Enginers, 1974, 1990.
F. Dusek: MATLAB a SIMULINK, uvod do pouzivani, Univerzita Pardubice, 2001, in Czech.
J. Balate: Automaticke rizeni, BEN, 2003, in Czech.
M. Holodniok, A. Klic, M. Kubicek, M. Marek: Metody analyzy nelinearnich dynamickych modelu, Academia, 1986, in Czech.
B.W. Bequette: Process Control: Modeling, Design and Simulation, Prentice Hall, Upper Saddle River, 2003.
D. Acheson: From Calculus to Chaos: An Introduction to Dynamics, New York : Oxford Univ. Press, 1997.
 Note:
 Timetable for winter semester 2019/2020:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Fri Thu Fri  Timetable for summer semester 2019/2020:
 Timetable is not available yet
 The course is a part of the following study plans: