PID control law

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]... 

Finally, it is often necessary that the servo system exhibit zero steady-state error. This quality can be achieved by adding a term due to the integral of the error. The reason this works can be understood by considering what would happen should a steady-state error occur. The integrator would keep increasing the input ad infimum. Instead, an equilibrium point is reached with zero error. The complete PID control law is then... 

Proportional-integral-derivative (PID) controllers are derived for the feedback control of inventory levels. The PID control law in discrete velocity form is given by the following relationship (Marlin, 1995) ... 

A second strategy for independently adjusting the set-point response is based on a simple modification of the PID control law in Chapter 8,... 

In general, as p increases, the set-point response becomes faster but exhibits more overshoot. When P = 1, the modified PID control law in Eq. 12-39 reduces to the standard PID control law in Eq. 8-17. 

As one example of Method 1, standard PID control laws can be modified by making the controher gain a... 

Unfortunately, a plant always has fundamental limitations which restrict the highest bandwidth (Ob that a feedback control system can achieve, even with the best possible control law. Fundamental limitations stem from the process itself, e.g., in the form of time delays 6 and right half plane (RHP) zeros z > 0. In addition, the phase lag of a plant imposes a limitation when low order controllers, such as PID-controllers, are employed. Assume the plant model can be written on the form... 

What is the corresponding control law for the series PID controller Qualitatively describe its response to a step change in e(t). 

In this subsection previous obtained results of PID are analyzed. The research previously achieved is used to perform function factor adjustments with the aim of obtaining better control laws. PID controllers are tested by using larger trajectories that include a set of the basic trajectories. Figure 10 shows PID results when tracking of the different five trajectories is commanded. Turning asymmetries can be caused because of differences between the right and left velocity models. 

Considering qualitative results, we suggest using a fixed control law for PID controllers... 

---