Ziegler-Nichols controller tuning paramete

Using the Ziegler-Nichols tuning parameters, we repeat the proportional controller system Bode plot ... 

It is well known that a nonlinear system with an external periodic disturbance can reach chaotic dynamics. In a CSTR, it has been shown that the variation of the coolant temperature, from a basic self-oscillation state makes the reactor to change from periodic behavior to chaotic one [17]. On the other hand, in [22], it has been shown that it is possible to reach chaotic behavior from an external sine wave disturbance of the coolant flow rate. Note that a periodic disturbance can appear, for instance, when the parameters of the PID controller which manipulates the coolant flow rate are being tuned by using the Ziegler-Nichols rules. The chaotic behavior is difficult to obtain from normal... 

A key to the successful application of a PID control is the tuning of parameters, Xp, Tp and Tp in Equation 13.5. To tune them properly, the Ziegler-Nichols method is used, which includes an ultimate-gain method and a step-response method. 

Click the Closed loop ATV bullet, start the simulation mnning, and click the Start test button. After several cycles, click the Pause button to stop the simulation and click the Finish test button at the bottom of the Tune window (see Fig. 3.79). The ultimate gain (3.73) and the ultimate period (4.8 min) are displayed, as shown in the left side of Figure 3.80. To calculate the controller tuning constants, click the Tuning parameters page tab on the Tune window and select either Ziegler-Nichols or Tyreus-Luyben. 

Equations for Calculating the Ziegler-Nichols Tuning Parameters for an Interacting Controller... 

Tuning Parameters Based on the Measurement of Ku and Pu Recommended by Ziegler-Nichols for a Noninteracting Controller... 

Why can you use the classical Cohen-Coon or Ziegler-Nichols techniques for tuning a digital PI or PID controller What is the additional tuning parameter introduced by the discrete nature of a process control computer ... 

The PID controller is the most commonly used feedback controller in industry, with three tunable parameters as stated previously. The integral component ensures that the tracking error, E t), is asymptotically reduced to zero, whereas the derivative component imparts a predictive capability, potentially enhancing the performance. Despite its apparent simplicity, the subject of PID controller tuning has been discussed in several textbooks and thousands of research papers since the landmark work of Ziegler and Nichols (1942). In practice, despite these developments, most PID controllers are tuned as PI controllers for several reasons. 

Automatic tuning needs identify the dynamics of a certain process. Usually Relay was mainly used as an amplifier in the fifties and the relay feedback was applied to adaptive control in the sixties. The exciting to a process loop make it reach the critical point. The critical point, i.e, the process frequency response of the phase lag of pi(it),has been employed to set the PID parameters for many years since the advent of the Ziegler-Nichols(Z-N) rule. From then several modified identification methods are... 

In this section, we decide on exactly which two frequencies to use in Equations (6.52)-(6.54) in order to solve for the PID controller parameters. Our ultimate objective is to produce a PID controller that achieves a close match between the actual and desired closed-loop performemce in the time domain. Which frequencies to use for PID design has been and remains an interesting question. The well-known Ziegler-Nichols frequency response PID tuning method is based on the crossover frequency of the process. However, we have found that, although the crossover frequency is very important from a stability point of view, lower frequencies are far more important from a closed-loop performance point of view. 

When tuning using the Ziegler-Nichols closed-loop method, values for proportional, integral, and derivative controller parameters may be determined from the ultimate period and ultimate gain. These are determined by disturbing the closed-loop system and using the disturbance response to extract the values of these constants. 

The developed control system exhibited good performance in all the tested conditions however, it was necessary to perform a more rational choice of the controller parameters so as to obtain improved closed-loop responses of the present membrane system. The Ziegler-Nichols tuning technique was initially used. The value of the proportional gain providing an oscillatory response was equal to 4.508, whereas the oscillation period... 

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