PID algorithm

The PID (proportional, integral, derivative) algorithm has been around since the 1930s. While many DCS vendors have attempted to introduce other more effective algorithms it remains the foundation of almost all basic control applications. 

The basic form of the algorithm is generally well-covered by academic institutions. Its introduction here follows a similar approach but extends it to draw attention to some of the more practical issues. Importantly it also addresses the many modifications on offer in most DCS, many of which are undervalued by industry unaware of their advantages. This chapter also covers controller tuning in detail. Several commonly known published methods are included but mainly to draw attention to their limitations. An alternative, well-proven, technique is offered for the engineer to use. 

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The integral action of a PID algorithm is designed to remove this offset. The integral action term is given by... 

Remote control units. These units are used to control unit processes. Basic control functions such as the PID algorithm are implemented here. Depending on other hardware components used, data acquisition capability may be required to perform digital control. They may be configured to supply process set points to single-loop controllers. Radio telemetiy may be installed to communicate with MUX units located at great distances. 

Figure 3. First control trial. The temperature and reactant flow rate profile are shown in dimensionless units for the first pilot plant control trial. The PID algorithm and batch start-up control strategy were modified as a result of this trial.

Figure 4. Results of the final control trial. Three pilot plant runs were made to fine tune the PID algorithm and control strategy. This illustrates the excellent temperature control achieved in the final trial, using the same dimensionless units used in Figure 3.

Optional) How would you implement the PID algorithm in a computer program ... 

Equation 7.241 is the velocity form of the PID algorithm and the equivalent transfer function is ... 

When one is tuning a controller, the form of the PID algorithm must be known. The three common forms of the PID algorithm are parallel... 

Differences in the PID algorithm, controller parameters, units, and other fundamental control functions highlight the importance of understanding the structure of the controller and the requirement of sufficiently detailed documentation. This is especially important for the controller but is also important for the field instruments, final control elements, and device tnat have the potential to affect the signal characteristics. 

When PID algorithms are implemented digitally, what used to be integration becomes summation, and what used to be differentiation becomes difference. The scan period of DCS systems is fixed at around 0.5 seconds or is selectable for each loop from under 0.1 to over 30 seconds. As digital controllers do not continuously evaluate the measurements, but look at them intermittently, this increases the dead time of the loop by two "scan periods" which are needed to calculate the "present" and the "previous" error. 

The coolant supply valve is generally a fail-open throttling valve when the PID algorithm output is 100% (which typically corresponds to 20 mA and 15 psig of air), this valve is fully closed. The coolant return valve is generally a fail-open on/off valve when the PID output for this valve (a discrete output) is on, the valve is closed. 

Unfortunately, this method of control does not solve any of the inherent problems of nonlinear, exothermic temperature control. But it does not prevent the use of any of the traditional remedies, such as adaptive gain, bidirectional gain, or anti-reset windup, since these are all modifications to the PID algorithm. 

The fuel amount is in a separate control circle by the heat demand or the boiler- resp. reflux temperature only. PID algorithms ensure stable control behavior without on/off-operation / /. 

Regulatory control node. This is the simplest node. It implements the simplest RCS node, one in which the behavior is purely reactive. It has a World model (the PID algorithm is a model, an empirical or heuristic model, but a model of the system under control), but this model does not predict the behavior. It only reacts to the current values of the plant and decides an action to be performed (there is no plan, it is just an action for the next time). It can be considered to have a KD where the model parameters are stored. Very simple preprocessing is performed (but some it is done as signal failure,...)... 

PID controllers are simple to implement and are extremely flexible and are used for processes ranging from refineries to spacecraft to electronic devices to power plants. The PID algorithm is quite computationally efficient, and much of the flexibility of a PID controller comes from the unique characteristics of proportional, integral, and derivative action (hence PID). 

The Instrument Society of America (ISA) standard for the PID algorithm in the position form is given as... 

The PID algorithm can also be applied in velocity form. Applying Equation (15.4) at t - At results in the following equation ... 

The position form of the PID algorithm calculates the absolute value of the output of the controller, whereas the velocity form calculates the change in the controller output that should be added to the current level of the controller output. The position and velocity modes are different forms of the same equation therefore, they are generally equivalent. The velocity form is usually used industrially. In general, DCSs offer the velocity form of the PID controller in three versions the velocity form in which P, I, and D are based on the error from setpoint [Equation (15.8)] the form in which only P and I are based on the error from setpoint [Equation (15.6)] and the form in which only integral action is based on the error from setpoint [Equation (15.9)]. 

PID control. Always determine the form of the PID algorithm being used. Select the PID modes P, always I, when the controlled variable should retiun to its set point D, for processes that are undamped, unstable, or have a very large ratio of dead time/time constant. 

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