PROCESS DYNAMICS AND CONTROL Fourth Year by Dr . Forat Yasir AlJaberi

1. PROCESS DYNAMICS AND CONTROLFourth YearbyDr. Forat Yasir AlJaberi University of Al Muthanna College of Engineering Chemical Engineering Department

2. Introduction A chemical process plant is an integration of various processing units (e.g. reactor, columns, exchangers, pumps, etc.) placed in a systematic manner whose objective is to convert a certain raw material into a useful product in safe and economical manner. Raw material Product To meet the plant objective, we need to satisfy some requirement: • Safety • Production specifications • Environmental requirements • Operational constrains • Economics PLANT

3. Issues (Purpose of the control system): Generally, there are three main issues could be dealt with the control system as explain below: • The influence of external disturbances. • Stability of a chemical process. • The performance of a chemical process. The objective of the control system, in this case, is to maximize the profit of the process by trying to maximize the desired product and minimize the undesired product and hence increase the process performance. Therefore, the control system should minimize the production cost, losses, wastage, energy requirement and human labor.

4. Classification of variables: Variables are generally classified into the following: 1. Input variables: They are divided into: • Load variables such as the inlet and outlet flow rate for a continuous stirring tank reactor. • Manipulated variables such as the flow of steam into a heating tank. 2. Output variables: They are divided into: • Controlled variables such as the temperature, pressure and concentration. • Uncontrolled variables such as the concentration of reactants in the dead zone of a batch reactor.

5. Control system design: In order to design an active control system, the following aspects should be clear to the design engineer: • Control objective such as a heating tank, distillation column, reactor, etc. • Select measurements according to the control object mentioned in the first step. • Select manipulated variables according to the measurements selected in the second step. • Select the control configuration according to previous steps. • The design of controller according to the process.

6. Laplace Transform: The Laplace transform converts integral and differential equations intoalgebraic equations, this is like phasors, but applies to: • General signals, not just sinusoids. • Handles a non-steady-state condition. Properties and formulas: • Linearity • The inverse Laplace transform • Time scaling • Exponential scaling • Time delay • Derivative • Integral • Multiplication by i • Convolution

7. Forcing functions: They are the load disturbances affecting the process and lead it to deviate from the steady state, and these disturbances could be accidental or imposed. Actually, there are infinite numbers of forcing functions, but in practice, only a few forcing functions are exposed. These are: • Step function. • Unit step. • Ramp function. • Pulse input. • Impulse function. • Sine wave forcing function. • Cosine wave forcing function.

8. Transfer function: The transfer function of a linear system could be defined as the ratio of Laplace transform of output variable to the Laplace transform of input variable setting all the initial conditions to be zero. C(S)   R(S) G(S)

9. First order system: (definition and classification) First order systems are those systems described by a first order differential equation that represents the system dynamic behavior with time. Modeling of chemical engineering processes: • To model any process, the following steps should be applied: • Applied the material and energy balances in case of the unsteady state. • Applied the material and energy balances in case of the steady state. • Obtain the a differential equation in terms of deviation variables. • Obtain the transfer function for the modeled systems.

10. Response of Second order systems: • Study the responses for several types of forcing function such as step change and ramp change. • Time response specification of second order system (under-damped) practically, second order systems are designed to be under-damped systems since these systems tend to return to the steady state as soon as possible. The transient response specifications should be understood.

11. Mathematical expressions of time response specifications: • Study the mathematical expression of: • Delay time. • Rise time. • Peak time. • Over shoot. • Setting time. • Decay ratio. • Period of oscillation. • The natural period of oscillation.

12. Steady state error analysis: • Study the steady state error for the following: • Steady state error for step input. • Steady state error for ramp input. • Steady state error for parabolic input. Steady state error for type-0, type-1, type-2 systems: Type of the system could be determined according to the open loop transfer function G(s) H(s). • Steady state error for type-0 system. • Steady state error for type-1 system. • Steady state error for type-2 system. There are advantages and disadvantages of static error coefficients.

13. Block diagrams: It is the pictorial representation of the relationship between the input and output of the physical system. Block diagrams consist of the following main parts: • Block • Summing point • Take off point • Forward path • Feedback path

14. Techniques of block diagram reduction: The techniques of block diagram could be explain as below: • Blocks in series. • Blocks in parallel. • Moving a summing point after a block. • Moving a summing point before a block. • Moving a take-off point ahead of a block. • Moving a take-off point. • Eliminating a feedback loop. • Interchanging of two summing point. • Moving a take-off point ahead of a summing point. • Moving a take-off point after summing point. There are a several steps that could be used to reduce the block diagram.

15. Stability: Stability is a very important characteristic of the transient performance of a system as every system has to pass through a transient stage for a small period before reaching steady state study of stability is very important to determine whether the system reaches its steady state after passing through transient. The Routh - Hurwitscriterion of stability: This creation tests the stability of a system by converting its characteristics equation into an array called "Routh array". There are a specified steps that should be followed to convert the characteristic equation of a system.

16. Frequency response analysis: When a linear system is subjected to a sinusoidal input, its response will appear in a characteristic equation which its quantities could be obtained from the transfer function as will be explained in detail. Bode diagrams: It is a convenient method to represent the frequency response of a system. It consists of two parts to be plotted.

17. Types of controllers: In order to keep the output of a system at desired value, the output of this system should be measured and compared with desired value to determine how far this output deviated from the desired value. Basically, there are three types of controllers exists as follows: • Proportional controller (PC). • Proportional – integral controller (PIC). • Proportional – integral – derivative controller (PIDC).

18. Nyquist plots: It is an alternative way of representing the frequency response characteristics. It uses Cartesian coordinate in two dimensions whose ordinate represents the imaginary axis and abscissa represents the real axis. There are specified steps for Nyquis plot construction depending on the overall transfer function of the system that must be found at first.

19. Measuring devices (sensors): The successful operation of any feedback control system depends upon good measurement of the controlled output and the uncorrupted transmission of the measurement to the controlled. • Flow sensors. • Pressure sensors. • Temperature sensors. • Composition analyzers. Controllers tuning: The choice of controllers parameters depends basically on the nature of process model which adjusted the controller parameters to attain a successful control. Zieglar-Nichols tuning is an example of tuning techniques which could be applied through specified steps.

20. References: • Process control, Pao C. Chan. • Process control- A practical approuch, Myke King. • Process dynamics and control, J.M. Dougles. • Process dynamics and control, Dale E. Seborg. • Process dynamics, modeling, and control, Babatunate A. Ogunnaike. • Process systems analysis and control, Donald R. Coughanowr.

21. With Best Wishes