PID regulator

In order to tackle the problem of uncertainties in the available model, nonlinear robust and adaptive strategies have been developed, while, in the absence of full state measurements, output-feedback control schemes can be adopted, where the unmeasurable state variables can be estimated by resorting to state observers. The development of model-based nonlinear strategies has been fostered by the development of efficient experimental identification methods for nonlinear models and by significantly improved capabilities of computer-control hardware and software. 

In the following, an overview of the above discussed linear and nonlinear approaches to temperature control of batch reactors is provided. 

The PID regulator is the most widely used feedback controller in industrial settings. The output of a PID controller is given by the composition of three different correcting terms (Fig. 5.1) a proportional term, an integral term, and a derivative term, i.e., 

Since actuators are subject to saturation, the phenomenon of integral windup must be properly tackled namely, if the controller outputs a command beyond the 

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PID controller the classical PID regulator (5.1) with a feedforward compensation of the desired reactor temperature (i.e., ypdes is added to the control input). 

Hagglund, T. K. J. Astrom (1985), Method and an apparatus in tuning a PID-regulator , United States Patent 4549123. 

The modern DDC controller has only the control function PID. PLC controllers used in process installations may contain more complex regulation functions, for example, the fuzzy or auto-tuning of PID functions. Most DDC controllers are self-sufficient and independent of the controllers or computer programs that are used for system configuration. 

We have to make a distinction here between electric controllers (e.g. PID controllers) with a proportional valve as actuator and mechanical diaphragm controllers. In a regulation system w/ith electric controllers the coordination between controller and actuator (piezoelectric gas inlet valve, inlet valve A/ith motor drive, butterfly control valve, throttle valve) is difficult because of the very different boundary conditions (volume of the vessel, effective pumping speed at the vessel, pressure control range). Such control circuits tend to vibrate easily when process malfunctions occur. It is virtually impossible to specify generally valid standard values. 

Even with the advanced PID control, regulation is never perfect. The system needs a difference between Cl and CO to react and with a small gain this difference can be large, so at least temporarily the control is partial. Moreover, an attempt to compensate for this, for example by increasing A3 in Eq. (5), may lead to instabilities, oscillations, etc. 

Therefore, the control loop shown in Fig. 5.28 was developed to solve the problem of symmetry control [121]. Two additional PID control loops are used to control the homogeneity of the reactive gas partial pressure because of appropriate regulation of the threefold gas inlet (top/center/bottom). The... 

The regulation of heat exchangers and heating jackets is performed by pneumatic regulation valves. It is realized by sequential PID controllers taking into account the oil temperature as well as the gas medium temperature. 

Response of a system with (a) proportional + derivative (PD) control and (6) proportional + integral + derivative (PID) control when the gain is 15 percent of the critical gain. Part (c) shov the response with PID control when the gain is 50 percent of the critical gain, a practical limit for good regulation. Compare these responses to that shown in Fig. 10 for simple proportional (P) control. 

Flygare et al. (1990) demonstrated ET monitoring of an affinity-adsorption procedure. Lactate dehydrogenase (LDH) was recovered from a crude solution by affinity binding to a N6-(6-aminohexyl)-AMP-sepharose gel. The LDH activity signal from the ET was used in a PID controller to regulate the addition of... 

The primary source of heat is hot water. The hot water is heated by direct steam injection in the hot water heater. Three PID controllers are used to control product temperature. The first control loop regulates the... 

The process of HTST pasteurization (Figure 5.5) is described in detail in Section 5.3. The variables used here are four temperature measurements (°C) and two PID controller outputs (mA). The hot water temperature, preheater outlet temperature of raw product, holding tube inlet temperature of pasteurized product and holding tube outlet temperature of pasteurized product are the output variables of the process (variables 1-4, respectively). The input variables of the process are the PID controller output to the steam valve (variable 5) that regulates the holding tube inlet temperature of product and the PID controller output to preheater hot wa-... 

Platinum resistance thermometers monitor the temperature, and a three-term tunable PID controller, which is RS232-linked to a PC, stabilizes the v ue at the set point to an accuracy of at least 0.1 °C by regulating the secondary heat transfer. The set point temperature can be prograimned, so that precise thermal cycling is available, or manually entered for step variation. The woridng temperature range is 5 C with a thermal response 0.2°C/s. 

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