PID Tuner (ver. 1.0)
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1 PID Tuner (ver. 1.0) Product Help Czech Technical University in Prague Faculty of Mechanical Engineering Department of Instrumentation and Control Engineering This product was developed within the subject Project II at Faculty of Mechanical Engineering of Czech Technical University in Prague in Department of Instrumentation and Control Engineering (U12110) by students Ondřej Kozák, Martin Roštejnský, Jaroslav Urban and Adam Kouba under the supervision of Ing. Jaromír Fišer PhD. PID tuner (ver. 1.0) is software that enables user to get many information about given system as its stability, rise time, oscillation capacity and many more. Controller tuner also gives to user a possibility to tune given system by one of possible methods and controllers types chosen by user. 1
2 Table of contents Table of contents Main window System parameters panel Coefficients 'a' Coefficients 'b' Input delay field System equation Characteristics of given system Main menu panel Basic characteristics PID tuning Help Information panel Window of basic characteristics Step response graph Bode plot Nyquist plot Root locus Window of PID tuning controller constants panel Control panel Tune button Approximation Characteristics load change button set-point change button overshoot 0% button overshoot 20% button Info panel Model panel Controller type
3 Controller tuning methods Disturbances Step response graph Compare field Legend pull down menu Disturbance window Main panel Apply button Cancel button Random coefficients button Disturbance transfer function panel ( G(s) d/y ) Coefficients of disturbance transfer function Clear button Info box Disturbance step response graph
4 1. Main window Main window contains configuration of users system and basic information and characteristics about given system System parameters panel The main system formula is specified bellow: a 4 y''''+a 3 y'''+a 2 y''+a 1 y'+a0 = b 0 fields. You can choose your own coefficients a i and b i by changing individual coefficient Coefficients 'a' Coefficients 'a' are rates of numerator of transfer function 4
5 Coefficients 'b' Coefficients 'b' is rate of denominator of transfer function. This version allows only one coefficient b 0, other coefficients will be implemented in later versions Input delay field This field and it is function will be implemented in alter versions System equation Formula of given system Characteristics of given system Stability: Your system could be stable or unstable Oscillation capacity: Your system could be oscillating or non-oscillating Lag time: Value of system lag time in seconds Lead time: Value of system lead time in seconds 1.2. Main menu panel Basic characteristics By pushing the button of basic characteristics the window of basic characteristics will be opened PID tuning By pushing the button of main characteristics the window of PID tuning will be opened Help By pushing the help button the PDF file with help will be opened 1.3. Information panel This function will be implemented in later versions. 5
6 2. Window of basic characteristics In this window you can see step response graph of given system by coefficients a and b of system transfer function Step response graph Displays step response for system specified by system polynomial chosen in main window, controller type, it's tuning method and chosen disturbances. Step response graph is generated through stepplot MATLAB function. Which makes it possible to get some basic information about system step response properties by pressing mouse right button. 6
7 2.2. Bode plot Displays magnitude diagram and phase diagram for system specified by system polynomial chosen in main window, controller type, it's tuning method and chosen disturbances. Bode plot is generated through bode MATLAB function. Bode plot allows user to get some basic information about phase or magnitude diagram properties by pressing mouse right button Nyquist plot Displays Nyquist plot for system specified by system polynomial chosen in main window, controller type, it's tuning method and chosen disturbances. Nyquist plot is generated through nyquist MATLAB function. Nyquist allows user to get some basic information about Nyquist plot properties by pressing mouse right button Root locus Displays Root locus plot for system specified by system polynomial chosen in main window, controller type, it's tuning method and chosen disturbances. Root locus plot is generated through rlocus MATLAB function. Root locus allows user to get some basic information about root locus plot properties by pressing mouse right button. 7
8 3. Window of PID tuning Serves for choosing tuning method, controller type, kind of disturbance and for comparing of more methods 3.1. controller constants panel Controller constants panel contains individual gains of controller: ro... proportional gain ri... integral gain rd... derivative gain where: Ti... integral time constant T d... derivative time constant These constants are set up automatically in dependence on properties of system, selected type of controller and controller tuning method after pressing the Tune button in Control panel. Only for tuning method manual you can set up constants manually. 8
9 3.2. Control panel Tune button After pressing Tune button controller constant will be tuned and set up on controller constants panel and the step response of system will be displayed in step response graph Approximation After pressing button the window of approximations will be opened Characteristics After pressing button the window of basic characteristics will be opened load change button Load change button serve for switching a tuning for the response to load change of CHR modification of Ziegler-Nichols tuning method set-point change button Set-point change button serve for switching a tuning for the response to set-point change of CHR modification of Ziegler-Nichols tuning method overshoot 0% button Overshoot 0% button serve for switching response without overshoot for one of the CHR modification of Ziegler-Nichols tuning method overshoot 20% button Overshoot 20% button serve for switching 20% for one of the CHR modification of Ziegler- Nichols tuning method 3.3. Info panel Info panel gives to user basic information facilitating his choose and information about passed choose. 9
10 3.4. Model panel Model panel displays form of model which contains system, controller, Input system disturbance and output system disturbance In panel it is possible to choose type of controller, controller tuning method or each disturbances Controller type Controller type selection is situated inside controller section in model panel. There are 4 possibilities to choose. ' - '... No controller No controller is used. Also feedback is disconnected in the model panel. After pressing Tune button only system with chosen disturbances will be displayed in step response graph. For this possibility you can't use any tuning method. 'P'... P controller Proportional controller is used. After pressing Tune button only proportional gain _ro_..._proportionalwill be tuned in controller constants panel. Integral and derivative gain is set up to zero 'PI'... PI controller Proportional integral controller is used. After pressing Tune button will be tuned proportional _ro_..._proportionaland Integral gain in controller constants panel. Derivative gain is set up to zero. 'PID'... PID controller Proportional integral derivative controller is used. All three gains (proportional, _ro_..._proportionalintegral, derivative) will be tuned in controller constants panel Controller tuning methods Controller tuning method selection is situated inside controller section in model panel. There are many possibilities to choose. All tuning methods are described below. Available methods: Ziegler-Nichols controller settings Cohen-Coon controller settings Lambda tuning settings AMIGO tuning settings Balanced tuning technique CHR modification of Ziegler-Nichols tuning settings Manual setting 10
11 Generally, these design relations are based on the characterization of the process to be controlled by its static gain K and its apparent time constant T and dead time T l, that is the process representation by a FOPDT (First-Order-Plus-Dead-Time) model. Used marking: K... static gain T... time constant T l... dead time K p...proportional gain T i...integral time constant T d...derivative time constant Ziegler-Nichols controller settings These relation for tuning P,PI and PID controllers have been published in Based on the data obtained from the process reaction curve they propose the following controller settings: Controller K P T i T d P - - PI - PID The Ziegler-Nichols formulas can also be applied for integrating processes that can be represented by transfer function including an integrator and apparent dead time, that later can be written as, or, since K has the dimension of the inverse of a time constant and can be replaced by ). Actually the step response of such processes is similar to the initial part of model response, since the slope of the latter has a maximum equal to K/T at the take-off. Therefore, with setting either K or T at 1 the same design relations can be used for such integrating processes and FOPDT processes. 11
12 Often, in the literature the Ziegler-Nichols formulas are presented with parameter, as follows: Controller K P T i T d P - - PI - PID Cohen-Coon controller settings In the fifties also G. H. Cohen and G. A. Coon proposed other controller settings with a view to the rejection of load disturbances with a quarter amplitude decay ratio. Their formulas are base on the same parameters, and T l as the Ziegler-Nichols formulas, hence again the difficulty to control the process. Controller K P T i T d P - - PI - PD* - PID * This type of controller is not used in this aplication Lambda tuning settings In the seventies C. L. Smith, A. B. Corropio and J. J. Martin proposed tuning relations as simple as the Ziegler-Nichols relations but including a tuning parameter λ. These relations can be written down as follows: Controller K P T i T d P - - PI - PID By changing a value of tuning parameter λ one can adjust the value of controller gain with a view to desired control aggressiveness, hence the shape of the closed-loop responses. 12
13 Recommended start values of λ are: for a P controller: λ=0 for a PI controller: λ=1 for a PID controller: λ=1.2 However, such PI and PID controller settings result into a poor rejection of load disturbances when the time constant T is highly dominant; then, the response to load changes is a small error with a very slow decay. This is a consequence of the fact that the process dominant time constant is more or less cancelled in the open-loop transfer function relating the process output variable to the load. Conversely, if the process apparent time constant T is negligibly small the proportional gain K p and integral time constant T i go to zero so that the PI controller as also the PID controller reduces to a plain integral controller with transfer function AMIGO tuning settings Balanced tuning technique CHR modification of Ziegler-Nichols tuning settings In the fifties K. L. Chien, J. A. Hrones and J. B. Reswick proposed some modification of Ziegler-Nichols formulas with a view to responses without overshoot or with 20% overshoot. Furthermore, they proposed to tune the controller either for responses to set-point changes or for the responses to load changes. Tuning for the response to load change Overshoot 0% 20% Controller K P T i T d K P T i T d P PI - - PID 13
14 Tuning for the response to set-point change Overshoot 0% 20% Controller K P T i T d K P T i T d P PI - - PID Manual setting By switching manual settings the fields of controller constants in controller constants panel are available to rewrite. Then user can set up his own controller constants Disturbances There are two possible disturbances to add to model. Input system disturbance (disturbance 1) and output system disturbance (disturbance 2). Adding disturbance: 1, To add required disturbance mark field 'use' in required disturbance section, then the set button will be available. 2, Press set button, then the disturbance window will be opened and press apply button disturbance is set up 3, set up disturbance transfer function in disturbance window 4, The disturbance window will be closed and required 3.5. Step response graph Displays step response for model specified by system polynomial chosen in main window, controller type, it's tuning method and chosen disturbances. Step response graph is generated through stepplot MATLAB function. Which makes it possible to get some basic information about system step response properties by pressing mouse right button Compare field If the compare field is marked next step response will be added to existing responses in step response graph. 14
15 Legend pull down menu By selecting "show" or "hide" option from the pull down menu user can decide to hide or show legend in step response graph. 15
16 4. Disturbance window Disturbance window serves to adding required input or output disturbance of given system. System with disturbance can be displayed with or without controller as solitary system without disturbances Main panel coefficients Main panel contains apply button, cancel button and button for random Apply button Apply button serves for confirming of entered data of disturbance transfer function in disturbance transfer function panel Cancel button Cancel button servers for closing disturbance window without saving data of new disturbance transfer function. Old disturbance transfer function will be used for calculation. If there was no disturbance set up before, after pressing tune button in control panel in window of PID tuning will be calculated without concrete disturbance 16
17 Random coefficients button By pressing random coefficients button coefficients in disturbance transfer function panel will be filled up by random numbers and step response graph of that disturbance will be displayed in step response graph 4.2. Disturbance transfer function panel ( G(s) d/y ) Contain fields of coefficients of disturbance transfer function and clear button Coefficients of disturbance transfer function It is possible to set up 6 coefficients of disturbance transfer function of formula specified bellow: where: b d0,b d1 a d0,a d1,a d2 T dd... coefficients of numerator of disturbance transfer function... coefficients of denominator of disturbance transfer function... dead time value of disturbance Clear button By pressing clear button, all coefficients of disturbance transfer function will be cleared Info box This function will be implemented in later versions 4.4. Disturbance step response graph Displays step response of disturbance transfer function specified by coefficients of disturbance transfer function in disturbance transfer function panel Step response graph is generated through stepplot MATLAB function. Which makes it possible to get some basic information about system step response properties by pressing mouse right button. 17
18 5. Window of approximation Here you can switch between available methods of approximation. 18
19 Bibliography 1. P. Klán, R.Gorez. Process control. Praha : FCC PUBLIC s.r.o., ISBN: P.Zítek, M.Hofreiter, J.Hlava. Automatické řízení. Praha : Vydavateklství ČVUT, ISBN: P.Blaha, P.Vavřín. Řízení a regulace I. Brno : Vydavatelství VUT. 19
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