Institute of Automatic Control and Robotics Faculty of Mechatronics laboratory Excercise AS-5 "Single loop control system of level in tank with free outflow of liquid Autors : PhD. Eng. Danuta Holejko, PhD. Eng. Jakub Możaryn, BSc. Eng. Michał Bezler. Warsaw 2016
Single loop control system of level in tank with free outflow of liquid The aim of the exercise is to execute, study static and dynamic properties, and then assess the quality of single loop control system of level in tank with free outflow of liquid. Quality will be rated based on the values of indices of transient response of a system caused by step change in the setpoint or disturbance. The aim of the research is to determine the effect of the type of control algorithm and on values of parameters (controller ettings) on the quality of the system. Identification of controlled system carried out in laboratory excerciseas-4 enables the selection of parameters (settings) PID controller implemented in the used SIMATIC S7-1200 PLC controller. Analysis of obtained indicators will allow the assessment of the accuracy of the compensation of the disturbances acting on the object and the precision of PV following the changing setpoint SP. 2
1. DESCRIPTION OF THE PROCESS / LABORATORY STAND Experiments were conducted on laboratory stand presented in Fig. 1. Controlled process is a change of liquid level in connected tanks Z1, Z2. Fig.5 presents installation diagram. Depending on the configuration of the valves V2 and V4 and the use of specially constructed elastic tube there can be realized process with various properties (see excercise AS-4). Figure 1. Installation scheme of the laboratory stand for designing the control system of the liquid level in a tank. Description : Z1, Z2 tanks, V1, V3 - manual outflow valves V2 - manual valve connecting tanks Z1 and Z2, V4 - threeway valve, W- elastic tube, T 0 - transport delay introduced by elastic tube, VE1- electromagnetic valve to cut-off the outflow from tank Z1. VE2 - electromagnetic valve to cutt-off the water outflow at the pump plunging. H1, H2 - height of the liquid column in tank Z1, Z2, PV output signal from the liquid level sensor, LT1, LT2 liquid level sensors in tanks Z1, Z2, Q - output signal from the flow sensor QT (Venturi flowmeter), 3
P- variable displacement pump, CV - pump control signal (output signal from PLC controller), P1, P2 - manual switches of electromagnetic valves to introduce disturbances. Components of the stand (Fig. 1) are: tanks Z 1 and Z 2, a pump P is controlled by standard current signal that corresponds to a change of the pump capacity 0-6.5 [l / min], LT 1, LT 2 are pressure transducers (measuring range 0-500 mmh20) for measuring a liquid level in each of tanks (H 1, H 2 ). W is the elastic tube, through which the liquid can flow into the tank Z 1 (it introduces the transport delay to the object). V 1, V 2, V 3, V 4 are manually operated valves, which are used to change the way that liquid flows. There are also two electromechanical valves (VE 1, VE 2 ), used to introduce disturbances into the process. By ZK 1 we denote leakage from the tank Z 1 (opening the valve VE 1 ), and by ZK 2 we denote leakage at pump outlet (opening the valve VE 2 ). Connection of the tanks is realized by using of shut-off valve V2. The controlled variable is the height of the column of liquid in the tank Z1 (H1) or tank Z2 (H2). Requirement for a system is to regulate it to keep at a preset constant value the height of water column despite the disturbances acting on the object. Disturbances are changes of the flow at the inlet or outlet of the tanks. These disturbances are carried out by remote-controlled shut-off magnetoelectric valves VE1, VE2. Opening / closinf of valves is realized using the P1 and P2 buttons located on the desktop stand. The valve VE1 induces a step change in flow at the outlet from the tank Z1. It is the fault VE1. The valve VE2 induces a step change in flow at the inlet to the tank Z1 (ie. liquid drop from the pump). It is the fault VE2. The control value of the object is a standard signal 4-20 ma from the controller Simatic PLC S7-1200 (Siemens). This signal is converted by a electronic circuit to the voltage signal 0-10 V and operate the pump, the output of which varies in the range: 0-6.5 l / min at the inlet to the tank Z1. This pump acts as an actuator in the control system. In addition, a flow measurement is carried out using a Venturi flowmeter. The flow changes from 0 to 6.5 L / min causes a pressure difference across the Venturi flowmeter in the range from 0 to 500 mm H 2 O. Applied differential pressure transducer converts the pressure difference across the orifice to a standard signal range of 4-20 ma. Information on the current value of the controlled variable (height H1 or H2 of the liquid column) is provided by electrical transducers with the range of 0-500 mm H 2 O and the output signal 4-20 ma (measuring the height of the liquid column is carried out using the indirect method by measuring hydrostatic pressure). 4
Figure 2. Electrical scheme of the control system of the liquid level in a tank. The laboratory stand include: tanks connected in series, SIMATIC S7-1200 PLC (Programmable Logic Controller) with the analog inputs / outputs module and power supply 24V, HMI display with a color touch screen, desktop PC with TIA Portal software. 5
2. Selection of the controllers settings Continuous controllers used in industrial practice are universal devices. Their parameters (settings) can be changed (adjusted) within a wide range, so they can work properly with objects of different dynamics. Depending on the set requirements for control quality, following settings should be adjusted: k p magnitude of proportionalm part [unitless], T i time constant of derivative part [s] T d time constant of integral part [s]. Abovementioned PID cotroller settings are ususally selected depending on requirements posed by the quality of controll according to different procedures (selection of settings). Based on theoretical considerations, modelling research and experience from system expolitation there were developed many rules for PID parameters choice depending on the specific model of the controlled process, type and location of disturbances, adopted criterion of quality and control algorithm. The most widely accepted criterion of control quality is transient response characteristics of the control system. There are usually taken into consideratino following types of transient responses: 1. aperiodic transient response with overshoot 0 5% and minimal control time t r, that provides a minimum of integral index e( t) dt, this is the criterion described as 0 IAE (Integral of the Absolute value of Error). 2. oscillatory transient response with overshoot 20% and minimal control time t r, that provides a minimum of integral index t e( t) dt ; this is the criterion described as 0 ITAE (Integral of the Time weighted Absolute Error), 3. transient response that provides a minimum of integral index e 2 ( t) dt min, with 0 overshoot 45% ; this is the criterion described as ISE (Integral of Square of the Error). When selecting settings for static processes, the important parameter is the ratio of delay time to substitute first order lag time constant T 0 /T z that characterizes susceptibility of the process to control action. When the ratio exceeds 0.3 the quality control with the best-chosen PID controller settings PID worsens significantly. In the exercise there will be applied the following methods of tuning: a) tabular method of tuning based on the experimental identification of the object (AS-4), b) The experimental method of Ziegler - Nichols. 6
Change of the setpoint SP Z(t)=1(t) 2.1. Tabular method of controller tuning This method requires knowledge of the parameters of process mathematical model. For the static model the parameters are k ob, T 0, T z. If we do not have theoretical description of the model, then we use tables or nomograms that require the prior identification of the process, eg. using step response on the basis of which one can determine the required parameters of the model. Knowing these parameters the controller settings are defined to ensure the required quality of control, eg. requirement oscillatory or aperiodic nature of the transient response of the control system. Tab. 1 summarizes the sample equations that define the set of regulators parameters for static processes. These formulas take into account the point of entry of disturbances. One set of parameters for provides a fixed set point control and as quickly as possible compensates the influence of disturbances, while the other should be chosen when the same system is to operate as a set point following system ensuring proper reproduction of the setpoint (SP) changes. e st0 Table 1. A list of formulas for setting controllers for the process G ob( s) k ob T z s 1 Type of the response Type of the controller k ob k p T 0 /T z T i / T 0 T d / T 0 = 0 % min t r = 20 % min t r = 0 % min t r = 20 % min t r P 0.3 - - PI 0.6 0.8 + 0.5 T z /T 0 - PID 0.95 2.4 0.4 P 0.7 - - PI 0.7 1 + 0.3 T z /T 0 - PID 1.2 2.0 0.4 P 0.3 - - PI 0.35 1.17 T z /T 0 - PID 0.6 T z /T 0 0.5 P 0.7 - - PI 0.6 T z /T 0 - PID 0.95 1.36 T z /T 0 0.64 7
2.2. Experimental Ziegler-Nichols method The method of tuning controllers developed in 1942 by Ziegler and Nichols is one of the most commonly used and widespread methods of experimental tuning of the PID controllers. This method is used when the controller and other elements of the actual control system are already installed, their functioning is tested (in manual control mode), and one should only choose the controller parameters. The method of Ziegler - Nichols (abbreviated Z-N) can be encountered in two variants: 1) the controller settings are selected on the basis of the parameters of the closed control system moved to the border of stability (using excitation system), 2) the controller settings are selected based on parameters defined the characteristics of the transient response of the control object due to the step input signal change (static processes only). In the exercise there will be applied Z-N method using excitation system. Within this method, the choice of the parameters is conducted based on the following steps: Step 1: In the manual mode (M) by changing control variable (CV), adjust the process variable (PV) to a state in which it is equal with the required setpoint (SP). Step 2: Set the controller to the proportional action (switch off integral and derivative actions), set the operation point control value of the controller equal to the setting obtained in the Step 1 and set the initial value of the controller gain k 0. Step 3: Switch the system to automatic control (A) and if the system maintains equilibrium, by changing SP produce an impulse with some amplitude and pulse duration depending on the expected dynamics of the process; observe or record the change in the controlled variable. It is recommended to use a pulse with amplitude of 10 % of the process value changes (PV) and pulse duration of about 10% of the estimated value of the time constant of the controlled process. Step 4: If the transient response is underdamped, set higher values of the proportional gain (Steps 1-3) until a system be on the border of stability (constant oscillations) - fig. 3c. Step 5: From the steady oscillations read 'critical' proportional gain k pkryt and oscillation period T osc. Step 6: Set the controller patameters according to the table of formulas developed by Ziegler-Nichols (Tab. 2). During the experiments there should be monitored if the control signal CV does not reach the limit values. If this happens, reduce the SP pulse parameters. The controller parameters are calculated on the basis of read values of using the formulas given in Tab. 2. p k pkryt and T osc, 8
a) b) c) Figure 3. Changes of the process variable (PV) obtained during Ziegler Nichols experiment Similar methods, based on experimental procedure, are implemented in modern microprocessor controllers or PLCs as the so-called autotuning. Table 2. Settings of the PID controllers according to Ziegler Nichols method Controller algorithm Z-N settings k p T i T d P 0.5 k pkryt - - PI 0,45 k pkryt 0.85T osc - PID 0.6 k pkryt 0.5 T osc 0.12 T osc 9
3.Visualization During the exercise the student communicates with the PLC via the operator diplay (SIMATIC HMI KPT600). On the Home screen, select an object tank (Zbiornik) and the single close-loop structure of a control system (Jednoobwodowy). After pressing the "Start" button, user go to the object visualization pressing the buttom "Tank" (Zbiornik) (Fig.4). Figure 4. Start screen (HMI KTP 600) Once the configuration is set, press button "Start" and go to the screen that shows the general structure of the system under study (Fig. 5). Figure 5. Structure of the single feedback loop control system. 10
Icons under the controller block indicate the current operating mode (Auto / Manual, Normal / Reverse, and Error acknowledge). After pressing controller block, one can go to the controller screenr (Fig. 6). Figure 6. Screen of the controller. Controller screen allows to change: - Algorithm of a controller by typing the appropriate setting, or selecting a mode in the "Type of control". - Switching of the controller mode: Auto / Manual. - Swiching the controller direction: Normal / Reverse. - Tuning procedures. - Reset of the controller parameters. In the right part of the screen are displays indicating the status of the controller. If the box "Error" is lit, the controller is in an inactive state. The most common cause of error is temporary opening in the measurement circuit. In this case, just replace the damaged cable and reset the controller by pressing the "Reset" button. Visualisation, in the form of plots the changes of the input and output values, is carried out on a PC using software TIA PORTAL. The home screen of this visualisation is shown in Fig. 7. 11
Figure 7. Start screen in TIA Portal simulation (HMI KTP 1200). The start screen (Fig. 7) contains information about the entered structure. When pressing "Regulator główny" button, user will be send to the screen with monitoring of the input and output variables (Fig. 8). Figure 8. Screen with monitoring of the input and output variables Over plots there is a graph showing the active disturbances in the form of a bar chart: Red rolor - valve VE1, Orange color - valve VE2, 12
Green color - "SP step function". 1. Start / Stop button allow user to stop or resume monitoring of the input / output values. 2. The Zwiększ przedział czasu ("Increase the time interval") and ("Decrease time interval") buttons allow user to modify the currently displayed time interval ranging from 15sec to 16min 3. The fields below the text Oś ("Axis") allow scaling of the Y-axis of the graph. Increasing the scope is performed immediately. In the case of reducing the scope of the scale the changes will be visible after some time. 4.. The "skok SP" ("SP step") button allows user to generate the step function of a setpoint, together with the monitoring of it in the upper graph. 5. The text next to the "Cofnij" ("Undo") button allows user to enter the value of the SP later activated the "Skok SP" ("SP step") button. After entering any of the values, do not change the value of this field before resetting the value by pressing "Cofnij" (""Undo") button. 6. The "Cofnij" ("Undo") button resets the step function activated by "skok SP" ("SP step") button. To print the chart, the course of the changing values should be stopped by START / STOP button, the user should press the button on a computer keyboard PrtSc and then paste saved screen into graphical editor. 13
4. Course of the excercise In the the exercise the controlled variable is the height H1 of the water column in the tank Z1 (represented by the value of the PV). Control signal CV generated by the SIMATIC S7-1200 Siemens is induced by: a. step change in flow at the inlet to the tank Z1 realized the opening of the valve VE2 (switch P1), b. a step change in flow at the outlet from the tank Z1 realized the opening of the valve VE1 (switch P2). Process properties were identified in out in the exercise AS-4. The control system pameters should be selected according to the quality requirements in accordance with the tuning procedure. 4.1. Tabular method of controller tuning Based on the results of the identification of the object carried out in the exercise AS-4 specify the parameters of the object identified with the tangent or secant methods (acc. to TA): k ob =..., T 0 =..., T z =... Using Table 1, calculate the settings of P/PI/PID controllers for transient response with overshoot 0% or 20% (as instructed by the TA) and write them into Table 3. Table 3. Calculated parameters of controllers. Controller = 0 % = 20 % type k p T i [s] T d [s] k p T i [s] T d [s] P PI PID 4.2. Starting the instalation Starting real plant control systems is usually carried out manually. The installed controller is switched by the operator to manual mode (MANUAL). Then the operator sets the controller algorithm, primary presets and planned for the installation setpoint SP, then, changing the control signal manual controls the process as long as the controlled variable PV reaches a permanent state established at a level corresponding to the desired setpoint SP. If all the devices included in the system are working properly and reached steady state is stable corresponding to a zero error, the operator switches the system from manual control to automatic control (AUTO). If the significant, abrupt changes are not observed and they are not beyond the certain limits of errors, then controller parameters shall be accepted as safe and start-up of the installation shall be considered completed. 14
In the controlled installation the operating point is the level of H1 25 cm (PV 60%),, which corresponds to the control signal CV 50%. To bring the system to the point of operation the following steps shall be performed: Step 1: Set up the system according to the diagram (Fig. 2). Step 2: Check the position of the switches P1 (fault VE1) and P2 (fault VE2), there shuld be no disturbance. Step 3: Set controller into MANUAL mode: MAN. Step 4: Set the panel CV (CV_man) = 50%. Step 5: Wait until the level in the tank will stabilize. Step 6: Set the setpoint SP = PV. Step 7: Enter the controller settings. Step 8: Set controller into AUTO mode: AUTO. If, when changing the mode of the controller to the AUTO mode, there will be quite significant changes in the control signal CV and the resulting changes in PV, switch controller in MANUAL mode. Then set the safe control value CV and repeat the starting procedure after finding the cause of a malfunction of the system, eg. wrong controller settings. 4.3. The study of the P controller and settings according to tabular method. 4.3.1. Check the efectiveness to compensate the disturbance VE1 Laboratory procedure is as follows: a) In the computer visualization choose observation of signals PV and SP. b) In the MAN mode, set CV_man = 50%. c) After the stabilization of liquid level in tank, enter the SP = PV and set AUTO. d) Switch P1 to open the valve VE1 (enter disturbance VE1). e) Wait until the value of measured PV will determine. f) At the computer visualization press Pause" ("Pauza") button to stop the trends. g) Save on PC the plots of PV and SP with marked time, when disturbance occured. h) Switch on the display of the control CV and save a plot of control signal. i) Switch P1 to close the valve VE1 (switch off disturbance VE1). j) Switch to MANUAL mode and set the CV_man = 50%. 15
4.3.2. Check the efectiveness to compensate the disturbance VE1 Laboratory procedure is as follows: a) In the computer visualization choose observation of signals PV and SP. b) In the MAN mode, set CV_man = 50%. c) After the stabilization of liquid level in tank, enter the SP = PV and set AUTO. d) Switch P2 to open the valve VE2 (enter disturbance VE2). e) Wait until the value of measured PV will determine. f) At the computer visualization press "Pause" ("Pauza") button to stop the trends. g) Save on PC the plots of PV and SP with marked time, when disturbance occured. h) Switch on the display of the control CV and save a plot of control signal. i) Switch P1 to close the valve VE2 (switch off disturbance VE2). j) Switch to MANUAL mode and set the CV_man = 50%. 4.3.3. Check the efectiveness of the control system to follow the process value PV after set point value SP. Laboratory procedure is as follows: a) In the computer visualization choose observation of signals PV and SP. b) In the MAN mode, set CV_man = 50%. c) After the stabilization of liquid level in tank, enter the SP = PV and set AUTO. d) Change the setpoint SP using the "Stroke SP" ("Skok SP") button e) Wait until the value of measured PV will determine. f) At the computer visualization press "Pause" ("Pauza") button to stop the trends. g) Save on PC the plots of PV and SP. h) Switch on the display of the control CV and save a plot of control signal. j) Switch to MANUAL mode and set the CV_man = 50%. k) Reset the SP using button "Back" ("Cofnij"). 16
4.4. The study of the PI controller and settings according to tabular method. Using the procedure described in section 4.3. choose the parameters of the PI controller based on Table 3, then repeat the study based on experiments from sections 4.3.1, 4.3.2, 4.3.3. The study can proceed after checking whether: a) the system is in operating point (CV = 50% PV 60%) (properly carried startup of installation). b) entered (via the HMI visualization) settings are entered properly for the PI controller 4.5. The study of the PID controller and settings according to tabular method. Using the procedure described in section 4.3. choose the parameters of the PID controller based on Table 3, then repeat the study based on experiments from sections 4.3.1, 4.3.2, 4.3.3. The study can proceed after checking whether: c) the system is in operating point (CV = 50% PV 60%) (properly carried start-up of installation). d) entered (via the HMI visualization) settings are entered properly for the PID controller 4.6. Experimental Ziegler-Nichols method Tuning based on Ziegler - Nichols method is carried out according to the following procedure: 1. Perform start-up procedure in manual mode (MAN) (acc. 4.2), set the CV = 50% and wait until a PV stabilizes. 2. The controller working with the process must be set to the P algorithm and a specific initial value of the proportional gain, eg. k p = 6, should be set, while all other regulator actions swithced off: T i 99999, 9, T d 0. 3. Manually set SP = PV. 4. In the computer visualization choose observation of PV and SP values. 5. Set the controller to AUTO. 6. Enter the impulse to change the setpoint, for example:. SP = 2-3% of the pulse duration t imp (Fig. 3) sufficient to cause noticeable changes of PV. CV signal during the test should not reach the limit values - in the opposite situation, the test must be repeated. 7. Evaluate the changes of PV and compare it with the course of signal from Fig. 3. 8. If the course of PV corresponds to Fig. 7c, save the PV plot in the computer and go to p.11. 9. If the course PV corresponds to Fig. 7a, the switch controller mode "MAN", set the CV = 50%, increase the gain k p, wait for PV to stabilize, adjust the SP to SP = PV and repeat steps p. 5-7. 10. If the course PV corresponds rys.7b, the switch controller mode "MAN", set the CV = 50%, reduce the gain k p, wait for PV to stabilize, adjust the SP to SP = PV and repeat steps p. 5-7. 17
11. Set the controller mode "MAN", set the CV = 50%. 12. Note the current value k kryt = k p that caused steady oscillations, then read the oscillation period T osc and calculate the controller settings P / PI / PID according to Tab. 2. Note: Any change of controller settings can be made only in MANUAL mode. Table 4. The results of the experiment and of the controller settings according to the Z-N method. Results of Z-N experiment k kkryt T osc P PI PID Controller settings k p T i T d 4.7. The study of the P, PI, PID controller and settings according to Ziegler- Nichols method Using the settings gathered in Tab. repeat the study based on experiments from sections 4.3, 4.4, 4.5. The study can proceed after checking whether: c) the system is in operating point (CV = 50% PV 60%) (properly carried start-up of installation). d) entered (via the HMI visualization) settings are entered properly for the P, PI, PID controller 18
5. REPORT The report shall contain the following elements: description of the exercises, diagrams, registered plots with data processing, graphs made on the basis of measurements, etc. Following questions should be answered: 1) Draw the block diagrams of the considered control system. 2) Draw the expected changes of process value PV and control value CV - induced by disturbance VE1 after the application of the P control algorithm and controller in Normal mode. 3) Attach and describe the results of the Ziegler - Nichols experiment. 4) Compare transient responses of control system and evaluate its static and dynamic. qquality. The quality should ne assessed on the basis of the readouts from the plots the following indices: e 1, e 2, e st, e m, t r, (overshoot). The results should be gatherred in table. 5) Compare the results obtained for the controller settings by tabular method and by the Ziegler - Nichols method. 6) Calculate the steady state errors based on the transfer fuction of the process and the transfer function of the controler and compare them with the values obtained from the experiments. 7) Calculate, based using the transfer fuctions of procees and controller values of k pkryt and T osc and compare them with the values obtained from Z-N experiment. 8) Answer the question: How from the plot of transient response caused by step change of the setpoint SP read the set value of the controllers' proportional gain k p? 19
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