发布时间 : 星期六 文章自动化专业毕业设计外文翻译--基于Ziegler Nichols自整定方法的参数的PLC更新完毕开始阅读a15e31041ed9ad51f01df2ce
Figure 4 Tolerance Limit
If the dead time is finished or calculated, the program starts to search maximum slope. It collects all slopes and after collecting them, it selects the biggest slope. Every slope is calculated with equation (5).
N?
Y(k)?Y(k?1)Ts (5)
It memorizes the output value of previous period and takes the output value of the recent period and divides their difference by sampling period [3, 5]. Then the program constitutes data of all slopes and selects the biggest slope. When the maximum slope is calculated, the program waits steady state because the parameters of system are stable in steady state. Finally, the program calculates PID parameters.
To sum up, to calculate PID parameters using Ziegler-Nichols PRM; first gather data from open-loop plant response to unit step input, then examine data set to find the maximum slope (Figure 3), after then determine the parameters needed for Ziegler Nichols PRM, finally, use tuning relations to generate PID constants.
Robustness of Ziegler-Nichols Method
A good PID controller design should exhibit robustness with respect to small
L/NMAXperturbations in the controller coefficients. Thus, the range of values that ensures robustness was determined for Ziegler-Nichols PRM in (6), where ? is system’s time constant (without controller) for first order deadtime systems (FODS),
Tand SET is settling time (without controller) for second order dead time systems (SODS) [3].
0?0?L?1.07forforFODSSODS? (6)
4.L?1.07TSET
Figure 5 Simulation Results of FODSs to the Step Response
1stSystem:0.3?0.3?1.0L0.32ndSystem:??0.5 (7)
?0.6L0.33rdSystem:??0.75?0.4?ndL
As seen in equations in (7) and figure 5, 2system is a more robust system than
rdstdo 1 and 3 systems due to L/? ratio. When L/? ratio increases from 1.07/2, system settling time is decreasing and when L/? ratio decreases from 1.07/2 system makes overshoot like a second order system, and when L/? ratio is approximately zero, systems make oscillation [2].
ndstIn equations in (8) and Figure 6, 2system is a more robust system than do 1 and 3 systems due to good performance due to
rd4L/TSET4L/TSETnd ratio. As resembling to figure 6, 2system has a ratio is approximately1.07/2.
Figure 6 Simulation Results of SODSs to the Step Response
1stSystem:2ndSystem:3rdSystem:4.L(4)(0.20)??0.26TSET3.054.L(4)(0.20)??0.43 (8) TSET1.854.L(4)(0.20)??0.74TSET1.08
From figures 6 and 7, Ziegler-Nichols process reaction method (PRM) always
provides a responsible proportional gain for PID controller. This method not only gives good performance but also is robust with respect to controller parameter perturbations [11].
Self-Tuning using Ziegler Nichols Process Reaction Method
PID parameters must be determined from dynamic system. As said before, system parameters change because of various reasons. If PID controller parameters remain the same for a long time, the dynamic system could not be controlled by PID efficiently. Root locus method, bode-frequency analysis method and some methods like this can be used for this calculation. But these methods have complex mathematical calculations, and also system feedback and system’s disturbationscan not be measured momentary without any error. In addition, system parameters (like system gain) change due to environmental change. For these reasons, a self-tuning PID controller is a necessity because this type of a controller can be used in different type of systems and environmental situations. Moreover, a self-tuning PID is a robust controller for systems’ uncertain parts. Also for changing at system dynamics the controller adopts itself. Thus, using a self-tuning PID is reasonable rather than using any other PID controller which has constant parameters [6].
Program algorithm for PLCs is given in Figure 8. The algorithm consists of two start options: one is working with recent parameters which are calculated before; other option is working with new parameters. In this option, program finds new PID parameters for system. Because of Ziegler-Nichols method is applicable for open-loop systems, program first cancels system feedback and waits the system response to settle. When the system output is reset, program records system’s momentary input and Then program applies a step signal to system input. It should be said that this step signal is at least 10% bigger than the systems current input (reference) value [11].
If the step signal smaller than 10%, system parameters can not be determined reasonable. After applying the step signal, program waits until the system output to settle at the output value. When the system output is stable, program calculates PID parameters using Ziegler-Nichols process reaction method and sends them to PID parameter input. When PID parameters are loaded, program attaches system feedback and PID controller. Thus, system starts to work with PID controller.
To clarify, necessary steps are given in a sequence below: - Run the system in open-loop mode - Wait until the system output becomes stable - Record system input and output
- Apply a step input to system (larger than of recent input)
- Wait until the system output becomes stable
- Calculate PID parameters and work with PID controller.
Adaptive Control
In everyday language, “to adapt” means to change a behavior to conform to new circumstances. Intuitively, an adaptive controller is thus a controller that can modify its behavior in response to changes in the dynamics of the process and the character of the disturbances.
In section 3, the Ziegler Nichols process reaction method gave three constant parameters of PID controller; Kc, Ti and Td. However, some system responses can be unpredictable, and these PID parameters can not work efficiently. Also, adaptive control can help deliver both stability and good response. The approach changes the control algorithm coefficients in real time to compensate for variations in the system itself. In general, the controller periodically monitors the system transfer function and then modifies the control algorithm. It does so by simultaneously learning about the process while controlling its behaviour.
Adjusting Adaptive Algorithm to the Self-Tuning Program
Self – Tune parameters, Adaptive algorithm and PI-D controller are related with each other like in figure 10. As said before, derivative parameter directly goes to PI-D controller, gain and integral terms firstly go adaptive algorithm and then PI-D controller.
Conclusions
In this article Adaptive PI-D controller - using Ziegler Nichols based Self Tuning method’s parameters- is presented and its application on a programmable logic controller is given. For this purpose first of all at the implementation part industrial PID algorithm is used where PID’s derivative input is taken from system output and filtered, so high-frequency signals’ effect is minimized. Then, integral term is confirmed to obtain a more robust PID structure and finally the output of PID is limited due to PLC’s maximum and minimum range. Secondly, Ziegler-Nichols method is given and together within robustness definition is defined. It can be seen that most industrial systems are in the group of this robustness limit. Adjusting adaptive algorithm to Self-Tuning PID Controller in section 4, the robustness limit is increased.