EXPERIMENT G1: Dynamic Response Modelling & Temperature Controller Tuning in a Jacketed Flow Reactor Objective This experiment involves a jacketed, mixed flow reactor in which an exothermic (heat generating) liquid phase reaction is taking place. Reactant flows into and product flows out of the reactor, on a continuous basis. A cooling jacket, with liquid coolant flowing in and out, serves to maintain the reactor at a constant temperature. Reactor temperature (the control variable in this case) may be controlled using a controller which measures the reactor exit temperature and manipulates the coolant flow rate in order to compensate for any process disturbances. Process disturbances are introduced as changes in the coolant inlet temperature. The purpose of this experiment is twofold: (i) to model the dynamic (time dependent) behaviour of this simple process by conducting open loop step response experiments; and, (ii) to utilise the process characteristics data obtained to tune the reactor PID temperature controller for optimum closed loop performance. The Control Station computer package is used for this experiment. This package allows for the real-life simulation of a jacketed flow reactor. Step response experiments are carried out in openloop configuration, and the resultant data are fitted to various quantitative theoretical response model equations in order to determine which of these is most appropriate for representing the process dynamics. The best fit from this procedure gives the process characteristic constants. Control Station is then used to calculate the optimum controller constant settings for the reactor temperature controller using an appropriate controller tuning correlation, and the performance of the tuned process control system is then examined. Theoretical Background The dynamic response of any process can be quantified by the used of an appropriate differential equation which expresses the behaviour of the system with respect to time. Thus for example for a process such as the liquid holding tank shown over, the level of liquid, h, in the tank can be shown to be dependent on the inlet flow rate, F, according to the following 1st order differential equation: h KF dt dh + = (1) where and K are characteristics (constants) of the process, called the time constant and process gain respectively. The value of the former is an indication of how rapidly the process responds to change, while the latter reflects the how sensitive the process is to change. F h Valve X Flow out Liquid Storage Tank: A First Order Process This type of process model is more generally called a first order process with the general (first order differential) equation: y Kx dt dy + = (2) where y is the process output variable, x is the process input variable, and t is time. More complex dynamic behaviours are shown by processes such as temperature control systems. Thus for example, the furnace control system shown below would exhibit a second order dynamic response behaviour according to the general equation: y Kx dt dy dt d y + 2 + = 2 2 2 (3) where is now called the period of oscillation, and is an additional process characteristic called the dampening factor. Temperature Controller Furnace Electrical power Thermocouple Furnace temperature Temp. setpoint Furnace Temperature Control: A Second Order Process Hence in this case if the set point temperature (input variable, x) is suddenly increased to a new value, then the furnace temperature (output variable, y) would respond according to equation (3). Simple first and second order processes represent only two of a variety of different process dynamic behaviours. For example, it is also possible to have a process which exhibits first order plus dead time behaviour. This type of process is similar to a simple first order one, except that the response of the process to an input change is additionally delayed by a period of time, termed the process dead time, td. Since both equations (2) and (3) are differential equations, they must be solved by integration in order to get the time response of the process (i.e. y as a function of t). The exact nature of the resultant solution will additionally depend on the nature of the input function (x). The latter can take the form of a step change (e.g. suddenly turn up the set-point temperature), ramp change (gradually increase the set-point temperature over time), or any number of other possibilities. The Control Station programme allows the user to fit equations such as (2) and (3) above to data obtained from the open loop process response experiment. Hence the best process model is determined, and values of the process constants are obtained. In addition it is also possible use the programme to obtain optimum controller constant settings for controlling this particular process. These may be determined using the process constants, in various ways, depending on the exact control objective, e.g. set-point tracking or disturbance minimisation. In this experiment the open loop response process characteristics (calculated for a first order plus dead time model, FOPDT) are used together with a selected empirical tuning correlation to give the optimal PID controller settings for process disturbance rejection. There are a number of tuning correlations available, including ITAE/IMC (integrated time absolute error/internal model control), and MPC /DMC (model predictive control/dynamic matrix control). The former is useful for single control loops, such as that used in this experiment, whilst the latter is more suitable for multi-loop control in larger processing units or whole plants. (See Control Station Help menu or a suitable process control text such as A Real-time Approach to Process Control by Svrcek et al, for more information on these tuning correlations). Experimental Note: in the text below = hit ENTER key. A. Starting the Control Station Programme 1. Double click on the icon marked Shortcut to Cstation. 2. Maximise the screen by clicking on the button in the top right hand corner of the screen and click on the Case Studies button. Select the Jacketed Reactor option. 3. Familiarise yourself with the various parts of the screen. Ask the lecturer/demonstrator for help if there is something that you don't understand. B. Dynamic Response Modelling (Open Loop) Initially the system is set up in open loop configuration in order to allow you to determine the most appropriate model for the reactor process itself (i.e. excluding the controller) 4. Open a file on your datastick to save your data into: click on the SAVE icon, choose the drive name that your datastick corresponds to, type in a file name, and click on Save. Choose OK for the 'Save simulation history?' box. 5. After the simulation has been running for a few seconds, make a step process input change by inputting the new value of cooling jacket inlet temperature given to you by the demonstrator. This may be done by clicking on the box, hitting the backspace keyboard key (), entering your value, and hitting Observe the process response, and when a new steady state output has been achieved for a few seconds, pause the simulation and click on the stop saving data button. 6. Click on the navigate button and choose the Design Tools option. This starts the model fitting part of the programme, where you can test out various process models to see which one best fits your open loop response data. 7. Open the file which contains you data by clicking on open data file button, selecting your named file and click on open. Note that your data is displayed in a number of columns labelled Time, Manipulated Variable and Process Variable. In this case you should assign the 5 th column of data (i.e. the cooling jacket inlet temperature) as your Manipulated Variable. This can be done by clicking anywhere on the 5th column of data and hitting the letter 'M' on the keyboard. The 5th column heading should then appear as 'Manipulated Variable'. Click on OK. 8. Minimise the Control Station screens by clicking on the _ button (top right hand corner of the screen). Start up Microsoft Word by double clicking on the appropriate icon. This will allow you to cut and paste your fitted modelling graphs directly into Word. 9. Return to Design Tools, click on the Select Model button, and choose the FOPDT (First Order Plus Dead Time) option and click on Done. 10. Start the fitting procedure by clicking on Start Fitting button. Eventually a graph showing your response data (white) and the fitted first order response equation (yellow) will appear. Note the degree of fit, as indicated by the value of the sum of squared errors (SSE) figure in the bottom right hand corner. The smaller this value is, the better the fit. 11. Transfer your plot to Word by clicking on Copy, ensuring that Metafile and Clipboard options have been selected, and then click on Export. Close the Print Data graph and maximise the Word file. Paste your graph into Word, and save your Word file to your datastick. 12. Return to Design Tools by closing the black graphical fit window. In the case of the FOPDT fit, you should save the model parameter and tuning correlation tables to a data file on your datastick, by clicking on the 'Save Fit' button, choosing the drive name that your datastick corresponds to, inputting another file name, and clicking on save. This is necessary since Control Station utilises the fitted FOPDT process characteristics from the open loop data to calculate the optimum PID controller settings using the various tuning correlation described above. Also write down the calculated optimum values of Kc, I , and D for PID Ideal (Noninteracting), for use later. 13. Repeat steps 9-11 for each of the following models: Second Order Plus Dead Time (SOPDT), and SOPDT Underdamped, each time cutting and pasting your results graphs into your Word file and saving it. C. Testing the Untuned Closed Loop Performance Now you can assess the closed performance of the reactor to an input change, when it is operating with a PID temperature controller. Initially we will just use the default controller settings, i.e. the controller will not be tuned (un-optimised). 14. Maximise the jacketed reactor screen again. Click on Run and choose 'Restart process using program defaults'. Click on TC (the temperature controller), choose PID, set the controller to ON for: Proportional - direct acting; Integral with anti-reset wind-up; and, Derivative On Ideal/Non-interacting. Click on done. Note that the process simulation diagram has changed to show that the controller is now connected up to manipulate the cooling jacket flow rate (and hence the reactor temperature) in a feedback control loop. 15. Pause the simulation, open another data file and re-start, running for a few seconds to obtain some initial steady state data. 16. Input again the value of cooling jacket inlet temperature given to you by the demonstrator and run the system until it reaches a new steady state. 17. Stop the simulation, and stop saving data to the file. D. Testing the Closed Loop Performance with Tuned (Optimised) Controller Settings 18. You can now try out the optimised tuned controller settings which you obtained in part B, step 12, and see if the process behaves in a optimal way in response to cooling jacket inlet temperature changes. Click on Run and choose 'Restart process using program defaults'. Click on TC (the temperature controller), choose PID, set the controller to ON for: Proportional - direct acting; Integral with anti-reset wind-up; and, Derivative on error. Also set Kc, I , and D to their optimum values (as noted in step 12 above), and click on done. 19. Pause the simulation, open another data file and re-start, running for a few seconds to obtain some initial steady state data. 20. Input again the value of cooling jacket inlet temperature given to you by the demonstrator and run the system until it reaches a new steady state. 21. Stop the simulation, and stop saving data to the file. 22. Exit the programme by clicking on the X button in the top right hand corner of the screen, and then clicking on the Exit Control Station button. Data Analysis/Discussion 1. Import the data in your data files into EXCEL. You may then use the graph function in EXCEL to plot up and store the untuned and tuned closed loop response data. Make sure that your plots are large enough and properly scaled so that the variations of the process parameter (reactor temperature) can be clearly seen as a function of time. 2. You should address the following issues in the analysis/discussion section of your write-up: Determine the best fit model for the open loop response data for this process. Consult a text on process control/modelling and see if you can explain why this model best fitted the dynamic response characteristics of this system. Compare the tuned and un-tuned closed loop response characteristics. Does the former show improvements in response behaviour? What features of the response profile could you quantify in order to verify any improvements or degradations in response behaviour? List and define at least three such features.