CONSIM - MS EXCEL BASED STUDENT FRIENDLY SIMULATOR FOR TEACHING PROCESS CONTROL THEORY

Transcription

1 CONSIM - MS EXCEL BASED STUDENT FRIENDLY SIMULATOR FOR TEACHING PROCESS CONTROL THEORY S. Lakshminarayanan, 1 Rao Raghuraj K 1 and S. Balaji 1 1 Department of Chemical and Biomolecular Engineering, 4 Engineering Drive 4 National University of Singapore, Singapore chels@nus.edu.sg ABSTRACT This paper highlights the capabilities and significance of a new e-learning tool developed at Informatics and Process Control research group. The main objective is to facilitate the students in simulating and experimenting different subject concepts in a new e-learning environment. It also aims at teaching students to make use of simple, economical and easily accessible spreadsheet tool like MS Excel for solving variety of Chemical Engineering problems. CONSIM standing for CONtrol SIMulator is an interactive training package developed using unique features of MicroSoft Excel, a widely used MS Office application tool. The CONSIM is used to mimic the real time chemical engineering system using steady state and dynamic models and employ known numerical solution techniques already learnt by students. The problem under consideration is observed to be interesting and of significance from chemical engineering education point of view. Hence user friendly spread sheet tool CONSIM can be successfully extended for simulating different design, optimization and analysis problems in chemical engineering education. Keywords: E-Learning, Chemical Engineering Education, Process Control, MATLAB, Excel, Simulator 1 INTRODUCTION Chemical Engineering is a vibrant field that has undergone significant changes over the recent years. The extensive progress made in traditional areas such as transport phenomena, reaction engineering and unit operations has provided enough experience for chemical engineers to confidently venture into new areas such as life sciences, rational product design, nanosystems etc. Computational methods and associated tools are expected to play a very significant role in this revolutionary phase of chemical engineering. A recent survey conducted amongst industrial practitioners and employers in Singapore s chemical and related industries (Lakshminarayanan and Farooq, 2004a) reflected the importance of computational skills among graduates. In other words, in a typical chemical engineering curriculum, students are expected to take core courses on topics such as mass and energy balances, fluid mechanics, reaction engineering etc. where mathematics play an important role. Most of the governing mathematical formulations and concepts should be easily visualized and understood by the students. The students can understand the basic concepts of many mathematics oriented subjects by solving or simulating the required equations or models using software. (Abbas and Al-Bastaki, 2002). In such cases, many students end up learning the software or trouble shooting the bugs in the software rather than getting useful information about their subject. Hence a very basic tool which is extremely easy for the students to develop their own programs will be helpful. In this work, we highlight the usefulness of Excel spreadsheet for this purpose. Due to its simplicity, Industries prefer Excel for macro creation and statistical analysis. The emphasis is on the use of embedded Visual Basic (VB) script with Excel as the interface for solving more complex models. The purpose of this paper is to demonstrate the use of Excel as a mathematical simulation tool. For this purpose, Excel is believed to have many advantages over other simulation programs. Software packages that use high level computer programming languages, such as MATLAB or Polymath require the user to have knowledge of high level programming languages. The single user license fees for such specialized packages further tax their availability. With the widespread utilization of readily and cheaply available MS Excel windows application tool such inherent problems with other simulation tools can be averted. Most students have previous experience using Excel and therefore are familiar with its operation. The user now can spend less time learning the software and more time mathematically simulating a process. Opportunities for using Excel as a steady state and dynamic simulation tool are abundant in course work and in research. Additionally, the widespread availability of Excel, both in computer labs and on students' personal computers, provides much more convenience in performing simulations in Excel than in other less accessible programs. Excel as a dynamic simulation tool in research is useful because of its adaptability to many different processes. Simulation of unit operations and processes can be achieved easily (Rosen and Partin, 2000 ; Jevric and Fayed, 2002 ; Lakshminarayanan, 2004b). The Excel simulation also aids in the development of processes in dynamic predictive modeling research. While Excel is not specifically designed for mathematical simulations, it has the capability to perform the calculations necessary for dynamic simulations. This is accomplished by using numerical methods to solve differential equations, integrals, and derivatives in a stepwise manner. Approximations like backward or central

2 difference method for derivatives can be used for implementation of derivatives in Excel. The accuracy in Excel is comparable to software packages using high level computer programming languages, as they use similar approximation methods for calculations. By allowing the users to input the equations by themselves, they gain a deeper appreciation and understanding of numerical methods. This article will discuss the development of the Excel simulation, the use of various numerical methods in Excel, and demonstrate how this simulation can be applied to a specific continuous-stirred tank reactor process and the design of a control system for the process. This mathematically simulated process illustrates how well the Excel simulation displays the information and how easy to manipulate certain information. As a case study, classical control problem of CSTR with PID controller is illustrated. A set of simultaneous differential equations have been developed for representing the dynamics of a CSTR carrying out general first order non isothermal reaction. The unsteady state temperature of the tank is controlled by a PID controller by adjusting the external heat input to the system. The model which forms a simultaneous ODE Initial Value Problem has been then solved using numerical techniques. The model is used to simulate various unsteady state dynamics of the system and results are analyzed by the students by changing the model and control parameters. System parameters like flow, volume are changed to see the effect on controller response. Controller Parameters like K c, τ d and τ I are adjusted to see the effect of the STEP and PULSE responses. Load change in inlet temperature (regulatory problem) and change in set point for tank temperature (servo problem) are simulated separately. Simple macros are written to develop interactive increase/decrease/reset buttons for changing different parameters for all the cases. Results for different case runs aid the student in establishing relevant concepts in process control, reaction engineering and numerical methods. Outputs and sample screenshots are shown in the paper. ((-r A ) = k C A ) is considered. The tank has external heating coil with heat input Q (kj/min) and the tank temperature is controlled by a PID controller in the closed loop feedback circuit as depicted in Figure 1. The temperature of the tank is measured at the outlet. Develop the mathematical model describing unsteady behavior of the entire reactor tank (Figure 1) when the system is disturbed using change in inlet conditions. Solve the model in order to obtain T Vs t capturing the dynamic behavior in absence (open loop) and in presence (closed loop) of P, PI and PID controllers. Analyze the performance by varying controller parameters and determine range for optimal operation. Observe the effect of kinetic parameters on the reactor performance. Do stability analysis for the tank temperature feed back control. 2.1 ASSUMPTIONS Ideal CSTR concentration and temperature everywhere inside tank is uniform The flow rate of the feed remains constant through out operation W i = W o = W Physical properties like C p and ρ are constant over the entire temperature range No phase change during the entire range of analysis. Heat losses to surroundings except the heating coil are neglected. The limit for Q is 0 to kj/min. Thermocouple used for analysis is first order in their dynamics. The heat of reaction is assumed to be constant over the temperature range assumed. The parameters and process variables are explained below with their notations along with the modeling steps. 2 PROBLEM SET UP The temperature control of a mixed tank system using a proportional controller was reported as a classical problem in chemical engineering seeking numerical recipe (Cutlip & Shacham, 1999). These problems are intended to utilize the basic numerical methods in problems which are appropriate to a variety of chemical engineering concepts and to aid the faculty in selecting the suitable software tool. The complexity of the problem has been enhanced in the current study by changing simple tank to a reactor carrying out known reaction and also complete controller (PID) mechanism has been adopted. The analysis is extended further to stability of the system and optimization of controller parameters along with a study on effect of reaction mechanism and other system parameters. A continuous stirred tank reactor with a non isothermal reaction A + B Products and with first order rate equation Fig. 1: Perfectly mixed tank reactor system with heater and temperature control 3 MODEL FORMULATION Reaction rate: 1 dn (-r ) = - V dt = KC A A A = dc - dt A

3 Set initial variables and parameters Get new K using Arrhenius model Solve for X A using kinetic model (1) Using new X A and K values calculate H r Step for T i Log T Vs t Solve (4), (5), (6) using difference formula to obtain new temperatures T, T o, & T m Calculate Q using old values (7) Fig. 2: Solution strategy for solving the set of formulated equations where k is the reaction rate constant (a function of temperature ) -E/RT k = k o e combining with unsteady state material balance dx A / dt = [-W/ρV]X A + k o e -E/RT (1 - X A ) (1) At t = 0, Q = Q s = WC p (T r T is ) + H r (2) where H r is the total heat liberated in tank (kj/min) An unsteady state energy balance on the stirred tank gives WCp (T i T o ) + Q + H r = d[v ρ C p T] / dt (3) Simplifying the above equation into ODE for T dt/dt = [ WC p (T i T) + Q + H r ] / [V ρ C p ] (4) where T, Q and H r are functions of time after the T i is disturbed and the new steady state is reached by the system itself or due to external control action which is to be considered next. In the control feed back as shown in Figure 1, the controlled variable T is measured at outlet as T o. The temperature variables are functions of time and need to be modeled before designing the controller. The tank temperature is measured at T o which is assumed to exhibit first order response to T with time delay and can be expressed as T o (t) = T(t - τ p ), where τ p is the process time delay. Using the Pade approximation for dead time results in differential expression for T o : dt o / dt = [T T o (τ p /2) (dt/dt)] * [2/τ p ] (5) with T o = T r at steady state The response for the measurement is given by dt m / dt = [T o T m ]/ τ m (6) with T m = T r at t = 0 (steady state condition at set point) Now T m is taken as input to comparator and the Error (E = T r T m ) is calculated. The controller output Q (the energy input to tank) as manipulated by the proportional/ integral / derivative (PID) controller modes can be described as t de Q = Qs + Kc *[ E + (1/ τ I ) E dt + τ D ] dt 0 where the integral error can be written as de sum / dt = E and hence the above equation becomes Q = Qs + Kc *[ E + (1/ τ ) E + τ I sum D de dt (7) with E sum = 0 at t = 0 (steady state value for error is zero). The above set of differential equations represents the complete dynamics for the system considered. The steady state system is disturbed by a load change on the system and the model is studied for the regulatory problem (external disturbance keeping set point constant). Inlet temperature of the feed stream T i is given a step change (at time t start = 10) using a step function available in math tools or by simply changing the value to a new value at given t. T i = T is T i = T is ± step size 4 SOLUTION STRATEGY ] for t < t start for t t start We can see that the set of equations with most of them being differential equations needs to be solved simultaneously. The step by step solution can be approached using the strategy as explained in the flow diagram in Figure 2. The above equations are solved using numerical methods for simultaneous ordinary differential equations with known initial values. Central difference formula is used for computing the differentials and the algebraic equations obtained there after are solved simultaneously to obtain the temperature set T, T o, T m at a given time interval t. The system model equations are logically coded and all the parameters & variables are defined and initialized appropriately as given in Table 1. The model and its solutions are developed using MS EXCEL spreadsheet. Backward difference formula is applied to evaluate direct derivative values to be used for getting temperature values at given time. The model developed is general in nature for any first order liquid reaction in the CSTR with external heating arrangement controlled by adjustable PID controller. Table 1, outlines the values used for simulating the system performance.

4 TABLE 1 : Process Variables and Default System Parameters for CSTR_TIC_ Simulation (data from Fogler (1992)) ρvc p 4000 kj/ C WC p 500 kj/min C k o 1 x min -1 E BTU/lb R BTU/lbmol F H r -1 kj/kg T is 60 C T r C ι p 1 min τ m 5 min Kc 50 kj/min C τ I 2 min τ d 5 min Step 30 o C Various system parameters are analyzed for understanding the dynamics of the CSTR under the influence of PID controller. System parameters like flow, reactor volume are changed to see the effect or controller response. Controller parameters like K c, τ d, τ I are adjusted to see the effect on the dynamic response for step and pulse disturbances for both (load changes in T i regulatory problem and change in set point T r servo problem) cases. Many combinations of system analysis can be done using the user friendly Excel Sheet (interactive provision for changing nine parameters for all four cases, refer Figure 4). 5 OBSERVATIONS Some of the simulation runs obtained from CONSIM are shown in Figure 3. Many interesting observations are possible by manipulating different parameters as shown in CONSIM screen shot Figure 4. Few are mentioned below. a) Increase in V (Volume of the tank) reduces oscillations, (slower response) flattens the curve in closed loop and the output for T shows steady state error. b) Increase in W (inlet flow rate) makes system more prone to disturbance and the peak of the PID response moves farther away from set point. System shows higher deviations. c) Higher values of system time delay push the system to have more oscillations and at higher values of τ P and τ m the system becomes unstable and exhibits diverging oscillations. d) P controller shows steady state offset and the error reduces as K c value increases. K c value above ~1200 for P controller leads to diverging oscillations. e) PI Controller resets the offset but brings oscillations into the system. Lower values of τ I parameter increases the frequency and amplitude ratio for oscillations. For I value of 2 min the system is critically stable for gain Kc ~ 0. f) PID Controller brings stability to systems and the oscillations are dampened. K c = 50, τ I = 2 and τ D = 5 exhibits best response for all the cases. 6 CONCLUSION The problem is observed to be interesting and of significance from chemical engineering point of view. The model comprises of set of ODEs with given initial values clubbed with other algebraic equations and posses challenge to numerical solutions. The set of equations are governed by certain assumptions and the operation is observed within these constraints. Different analysis carried out by varying many parameters give satisfactory results in line with control theories. Hence the mathematical methods studied in the course can be used successfully as tools for simulating chemical engineering problems which can be further applied for optimization and feasibility studies and better understanding of concepts. CONSIM provides better control and user friendly options to analyze the system dynamics. The simulated CSTR spread sheet built here in the work can be effectively used as training tool to explain various concepts of PID controller and tank dynamics. REFERENCES Abbas, A. and Al-Bastaki, N. (2002) The use of software tools for ChE education: Students' evaluations, Chemical Engineering Education, 36 (3), Cutlip M. and M. Shacham, (1999). Problem Solving in Chemical Engineering with Numerical Methods, Prentice Hall publications, Englewood Cliffs, NJ. Fogler, H. S. (1992). Elements of Chemical Reaction Engineering, 2nd ed., Prentice Hall,Englewood Cliffs, NJ: Jevric, J. and Fayed, M.E., (2002) Shortcut distillation calculations via spreadsheets, Chemical Engineering Progress, 98 (12), Lakshminarayanan, S. and Farooq, S. (2004a). Computing in NUS Chemical and Biomolecular Engineering Department: Benchmarking with universities and industrial needs, Proceedings of the first international conference on Teaching and Learning in Higher Education, Singapore, 1-3 December Lakshminarayanan, S. (2004b). Critical assessment of a new approach in teaching first course on process dynamics and control, Proceedings of the first international conference on Teaching and Learning in Higher Education, Singapore, 1-3 December MATLAB Release 14, (2005). The MathWorks Inc., Natick, MA. Rosen E.L. and Partin R. L. (2000). A Perspective: The Use of the Spreadsheet for Chemical Engineering Computations, Ind. Eng. Chem. Res., 39, g) The reaction parameters do not affect the response much as the change in conversion is negligible (<0.5%). Higher values of E and k o lead to instability.

5 SERVO PROBLEM - PID Response Pulse Size = 30 : Kc =, I = 1, D = Set Point SERVO PROBLEM - PID response Step Input (+ 20) : Kc = 50, I = 2, D = Set Point REGULATORY PROBLEM - Pulse Input (30) PID Response : Kc = 20, I = 2, D = Feed REGULATORY PROBLEM - Step input (+10) PI Response : Kc = 50, I = 2 D = REGULATORY PROBLEM - Step input (-20) PI Response : Kc = 50, I = 0.29 D = 0 - critically stable SERVO PROBLEM - PID response - Unstable Step Input (+ 20) : Kc = 1100, I = 1, D = Set Point Fig. 3: Simulation results obtained from CONSIM for various operating conditions Notation: T i : Inlet fluid flow temperature ( C) T : CSTR Temperature (Controlled Variable) ( C) T o : Outlet fluid flow temperature ( C) T m : Measured Temperature ( C) Q : Rate of heat input to tank (Manipulated Variable) (kj/min) k : Reaction rate constant (min -1 ) H r : Heat of reaction (kj/min) X A : Conversion of reactant A W : Total Fluid Flow rate (kg/min) ρ : Fluid density of feed mixture (kg/m 3 ) Cp : Specific heat of liquid (kj/kg K) V : Reaction volume of the tank (m 3 ) Tr : Set point for controlled variable ( C) τ p : Time delay in T measurement at output (min) τ m : Time constant for measuring device (min) τ I : Integral time constant in PID (min) τ D : Derivative time constant in PID (min) K c : Proportional Gain (kj/min K)

6 Fig. 4: Screen shot of the CONtrol SIMulator developed PROCEEDINGS OF THE 11 th APCChE CONGRESS 2006