Three Mode PID Controllers

In many process control applications, the control algorithm consists of three modes proportional (P), integral (I), and derivative (D). The ideal PID controller equation is 

Derivative control action is also referred to as rate action, preact, or anticipatory control. Its function is to anticipate the future behavior of the error signal by considering its rate of change. Derivative action is never used alone, but in conjunction with proportional and integral control. Derivative control is used to 

---

A capsule summary of the merits of the three kinds of corrective action can be made. The proportional action is rapid but has a permanent offset that increases as the action speeds up. The addition of integral action reduces or entirely eliminates the offset but has a more sluggish response. The further addition of derivative action speeds up the correction. The action of a three-mode PID controller can be made rapid and without offset. These effects are illustrated in Figure 3.3 for a process subjected to a unit step upset, in this case a change in the pressure of the control air. The ordinate is the ratio of the displacements of the response and upset from the set point. 

It is clear from the above that a three-mode PID controller should be the best. This is true in the sense that it offers the highest flexibility to achieve the desired controlled response by having three adjustable parameters. At the same time, it introduces a more complex tuning problem because we have to adjust three parameters. To balance the quality of the desired response against the tuning difficulty we can adopt the following rules in selecting the most appropriate controller. 

Supervisory control The selection of set points, usually to maximize profitability or minimize costs. Three-mode (PID) control A feedback control algorithm that uses proportional, integral, and derivative action on the error signal. 

An ideal three-mode PID (proportional, integral, and derivative) feedback controller is described by the equation ... 

PID action should be employed for systems which respond rather sluggishly. The presence of the derivative term allows a higher proportional gain to be used which will speed up the control action. Such controllers are frequently installed because of their versatility and not because analysis of the system has indicated the need for the presence of all three modes of control. 

In Example 8.12, we used the interacting form of a PID controller. Derive the magnitude and phase angle equations for the ideal non-interacting PID controller. (It is called non-interacting because the three controller modes are simply added together.) See that this function will have the same frequency asymptotes. 

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

Frequently all three modes are used together as PID control, i.e. ... 

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)]. 

The most commonly used analog controller is the three-mode proportional-integral-derivative (PID) controller. Its general form is given by eq. (13.6) ... 

The three-mode controller has a proportional and an integral character with derivative action (PID). The output signal of a PID controller is... 

Three-Mode Controller (PID Proportional, Integral, and Derivative)... 

Control algorithms We have discussed that in closed-loop control systems a corrective action is taken by the controller in response to feedback from a transducer. The exact corrective action depends on the algorithm which has been developed. The simplest control approach is a two position control which turns the control element on and off based on the monitored value of the output. With an on/off strategy, the process value will typically oscillate above and below the set point. The most common controller is the PID (proportional, integral, and derivative) loop controller which is able to detect an early trend, adjust quickly, and prevent an over-correction. A PID controller can maintain temperatures within 1°F. The controller provides the means to define the control algorithm by assigning a constant for each of the three control modes. Typically, most of the adjustment is accomplished with the proportional control element, with the control action, u be-... 

Note that the controller parameters for the expanded form are three gains, Kc, Kj, and Kjy, rather than the standard parameters, Kc, t/, and td. The expanded form of PID control is used in MATLAB. This form might appear to be well suited for controller tuning, because each gain independently adjust the influences only one control mode. But the well-established controller tuning relations presented in Chapters 12 and 14 were developed for the series and parallel forms. Thus, there is httle advantage in using the expanded form in Eq. 8-16. 

PID control The modes of control used to control processes or part of a process. The three basic modes of control are proportional control, integral control, and derivative control. Derivative control is always used in combination with proportional control or both proportional and integral control. Integral control is generally used in combination with proportional or with both proportional and derivative control. PID control is also known as three-term control. 

The main reason for interest in derivative action is to combine it with proportional and integral action to produce a three-mode controller, a PID. 

The three-mode or PID control is one of the most powerful but complex modes of operation. This mode is a combination of proportional, integral and derivative control modes and thus enjoys the advantages of each of these control systems. The PID mode can be represented by Eq. 7.11. 

---