Ziegler controller tuning

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

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... 

There are two very popular ways to control systems with inverse response the first uses a PID feedback controller with Ziegler-Nichols tuning and the second uses an inverse response compensator. 

Example 18.4 Controller Tuning by the Ziegler-Nichols and Cohen-Coon Methods... 

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. 

The TC2 temperature controller is tuned at the low-flow conditions since this is where it is active. Ziegler-Nichols tuning is used so that the tightest possible temperature control is achieved. Base and reflux-drum level controllers are proportional with Kq = 2. 

Ziegler-Niehols settings were calculated for each PI controller. Closedloop responses were foimd to be a little too underdamped, so the integral times were increased by a factor of two. Controller tuning parameters are given in Table 3. 

Because a proportional only controller will never reach SP, the quarter decay is determined with respect to the steady state condition. The reciprocal of the coefficient, in this case the reciprocal of 0.5, is known as the gain margin. It is the factor by which the controller gain can be increased before the controller becomes unstable. A proportional only controller tuned according to the Ziegler-Nichols method will therefore have a gain margin of 2. 

The most well-known tuning guidelines that make use of these concepts are the Ziegler Nichols method and the Cohen-Coon method. There are also other controller tuning guidelines, such as dead-beat tuning and Internal Model Control tuning. It is beyond the scope of this chapter to discuss the last two methods. 

Two early controller tuning relations were pubhshed by Ziegler and Nichols (1942) and Cohen and Coon (1953). These well-known tuning relations were developed to provide closed-loop responses that have a 1/4 decay ratio (see Section 5.4). Because a response with a 1/4 decay ratio is considered to be excessively oscillatory for most process control applications, these tuning relations are not recommended. 

Blickley, G. J., Modern Control Started with Ziegler-Nichols Tuning, Control Eng., 38 (10), 11 (1990). 

In 1942, Ziegler and Nichols [1] changed controller tuning from an art to a science by developing their open-loop step function analysis technique. They also developed a closed-loop technique, which is described in the next section on constant cycling methods. 

In 1953, Cohen and Coon [2] developed a set of controller tuning recommendations that correct for one deficiency in the Ziegler-Nichols open-loop rules. This deficiency is the sluggish closed-loop response given by the Ziegler-Nichols rules on the relatively rare occasion when process dead time is large relative to the dominant open-loop time constant. 

The following is a step-by-step approach to using the Ziegler-Nichols closed-loop method for controller tuning ... 

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... 

Table 16.1 Settings of both PI and PID controllers calculated by the Ziegler-Nichols tuning rule...

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

Using the first order with dead time function, we can go ahead and determine the controller settings with empirical tuning relations. The most common ones are the Ziegler-Nichols relations. In process unit operation applications, we can also use the Cohen and Coon or the Ciancone and Marlin relations. These relations are listed in the Table of Tuning Relations (Table 6.1). 

Ziegler-Nichols Continuous Cycling (empirical tuning with closed loop test) Increase proportional gain of only a proportional controller until system sustains oscillation. Measure ultimate gain and ultimate period. Apply empirical design relations. 

We have yet to tackle the PI controller. There are, of course, different ways to find a good integral time constant. With frequency response, we have the handy tool of the Ziegler-Nichols ultimate cycle tuning relations. So with Kcu = 60 and cocg = 3.3 rad/min, we find by referring to... 

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