The PID Controller

Fuel cell control options with feed-forward and feedback configurations using a look-up table, 

The parameters are related to the parameters of the standard form through 

Ky and are proportional, integral, and differential gains, respectively. The PID is fine-tuned using some preconceived ideal response profile for the closed-loop system. 

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With the exception of pneumatic controllers for special applications, commercial single-loop controllers are almost entirely microprocessor-based. The most basic products provide only the PID control algo-... 

This is the speed controller block that consists of both a PID (proportional integral derivative, a type of programming) controller and an acceleration compensator. The required speed reference signal is compared with the actual speed signal obtained from the motor model (section 2). The error signal is then fed to both the PID controller... 

The selection of the PID controller parameters K, T[ and can be obtained using the classical control system design techniques described in Chapters 5 and 6. In the 1940s, when such tools were just being developed, Ziegler and Nichols (1942) devised two empirical methods for obtaining the controller parameters. These methods are still in use. 

The Appendix shows how the CMVC (Eq. 10) can be recast into the PID controller (Eq. 12) using some simple approximations and algebra. For the present system, we used this procedure to calculate the following PID controller... 

Figure 5. Experiences at production scale. When (B) the Jacket coolant temperature (- -) dropped due to a plant modification, the reactant flow rate (- ) was increased automatically by the PID controller and maintained the reactor temperature (- in (A)) within 1 % of the setpoint.

Turning to Eq. (11), the general velocity form of the PID control equation, we can collect terms of like order in e, e and e to... 

Two PID controllers were then added to the reduced order model. Temperature at node 5 was paired with output 1, and temperature at node 55 was paired with output 2. The code required to realize the PID controllers is ... 

Example 5.7B What would be the PID controller settings for the dye mixing problem if we use IMC-based tuning relations ... 

For curious minds The first time you use the PID controllers, drag the icon onto a new simulation window, select the icon and then Look under mask under the Edit pull-down menu. You will see how the controllers are put together. The simple PID controller is... 

The PID controller combines the three individual modes to achieve the advantages of each. 

Shaw, J.A., The PID Control Algorithm How It Works and How To Tune It., 2nd edition, eBook, Process Control Solutions (www.jashaw.com). 

Try to operate the reactor isothermally with the PID-control as programmed to control the heat input rate. 

Fig. 6.18. Temperature tracking in the PID control mode one hotplate is kept at constant temperature, the temperature of the second microhotplate is modulated in a sinusoidal way. Rectangular temperature steps are applied to the third microhotplate...

Control is improved when the PID controller is used. There is less deviation in the controlled variable because the manipulated variable changes more quickly. As discussed above, if rapid and large changes in the manipulated variable cannot be tolerated, derivative action cannot be used to improve the control performance. 

Figure 10.9 shows the time-domain performance of these PI and PID controllers. The disturbance is a step change in Qp. Note the improved dynamic performance of the PID controllers. 

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... 

The most widespread type of controller is the PID controller. Here P stands for proportional, I for integral and D for differential control function. In the following some of the properties of this controller are described in detail. Information on the system behavior is gained through a step response to a control fault in certain controller settings. 

Proportional-lntegral-Derivative Control The most common algorithm for control action in the feedback loop of processing industries is the PID control, which is a combination of proportional action (P), integral action (1), and differential action (D). 

The PID control law considered here contains the P, PI, PD, and PID control laws as special cases. The velocity form of the discrete approximation of an ideal PID controller is given by [2]... 

We first assume that initial values of the controller parameters have been obtained using any classical control technique. We then introduce tuning factors <>]. j and 9f as well as the binary variables 8P, Sj., and 5° to denote the selection l-th term of the proportional, integral and derivative term of the PID controller, i.e. 

W.L. Luyben, Effect of derivative algorithm and tuning selection on the PID control of dead-time processes, Ind. Eng. Chem. Res. 40 (2001) 3605-3611. 

More typically, instead of setpoint changes, the regulatory problem of responding to a system disturbance is encountered in commercial reactors. For this reason, the optimum tuning constants for the PID controller were developed from the IAE ralations for load disturbances. First, however, it is necessary to obtain a process model of the system. Brantley (10) has developed a process identification technique which fits process data to the second order plus dead-time form ... 

Proportional-plus-Integral-plus-Derivative (PID) Control The derivative mode moves the controller output as a function of the rate of change of the controlled variable, which adds phase lead to the controller, increasing its speed of response. It is normally combined with proportional and integral modes. The noninteracting or ideal form of the PID controller appears functionally as... 

The variability of the process parameters with flow causes variability in load response, as shown in Fig. 8-50. The PID controller was tuned for optimum (minimum-IAE) load response at 50 percent flow. Each curve represents the response of exit temperature to a 10 percent step in liquid flow, culminating at the stated flow. The 60 percent curve is overdamped and the 40 percent curve is underdamped. The differences in gain are reflected in the amplitude of the deviation, and the differences in dynamics are reflected in the period of oscillation. 

In order to analyze the effects of different estimates of aq on the control scheme, the cascade controller (5.45)-(5.47) is used in conjunction with the three different observers presented in Sect. 5.6. Finally, the results are compared with those obtained by using the most widely used industrial controller, i.e., the PID controller. Therefore, five different control schemes have been compared ... 

Figure 5.8 is referred to the performance of the PID controller. It can be recognized that the temperature tracking error is always below 0.5 K and is characterized by a very similar time history of the control input with respect to the previously tested schemes (Fig. 5.5). By comparing the results in Fig. 5.8 with those in Fig. 5.4, the adaptive model-based scheme presents better performance than the linear PID control, especially during the heating and cooling phases, i.e., when the reference temperature is not constant.

The results are shown in Fig. 5.9 as a function of the set-point temperature for both the model-based and the PID controller. In both cases, the critical 6 increases with the setpoint temperature since a more efficient heat exchange is required when... 

Fig. 5.9 Safety boundaries for the phenol-formaldehyde reaction when the temperature reactor is controlled by using the model-based adaptive strategy and the PID controller...

Many, more advanced, technical systems make use of a combination of all three types proportional, integral and differential control. This is called the PID control [1-3]. The expression for CC becomes then ... 

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