28-07-2012, 03:59 PM
PID Controller Design PID
[attachment=29419]
Introduction
The PID Actions
A typical structure of a PID control system is shown in Fig. 6.1, where it can be seen that
in a PID controller, the error signal e(t) is used to generate the proportional, integral, and
derivative actions, with the resulting signals weighted and summed to form the control
signal u(t) applied to the plant model. A mathematical description of the PID controller .
PID Control with Derivative in the Feedback Loop
From Fig. 6.4(b), it can be seen that there exists a jump when t = 0 in the error signal of the
step response. This means that the derivative action may not be desirable in such a control
strategy.
Thus, in practice, the derivative term may be preferred in the feedback path. Since
the output does not change instantaneously for a step input a smoother signal is produced by
taking the derivative of the output. This PID control strategy, which will be denoted PI-D,
is shown in Fig. 6.5.
Recall the typical feedback control structure shown in Fig. 1.2. The controller and
feedback transfer functions can be equivalently written.
Methods for First-Order Plus Dead Time Model Fitting
It can be seen that the model (6.5) is useful for designing a PID controller because of
the availability of a simple formula. The method in Sec. 6.2.1 for finding L and T of a
given plant is simple to use with the graph of a plant step response. Although in modern
computation it is not necessary to reduce a model to this form to find suitable PID controller
parameters, which may be found by using the original model with one of many possible
approaches, nevertheless it can be useful. Given the plant transfer function, we can use
one of the model reduction methods described in Chapter 3. For example, the suboptimal
reduction method [47] is very effective at the expense of an affordable heavy computational
load. The optimal reduced-order model can be obtained with the function opt_app(),
covered in Sec. 3.6. In this section, two other effective and frequently used algorithms will
be introduced.
A Modified Ziegler–Nichols Formula
Consider the Nyquist frequency response shown in Fig. 6.12(a), where for a selected pointA
on the Nyquist plot, the control effects of the P, I, and D terms are shown in the appropriate
directions. Thus, with properly chosen Kp, Ti, and Td, it is possible to move the given point
A on the Nyquist curve of the uncontrolled plant to an arbitrary position on the Nyquist
plot of the controlled system. The typical Nyquist plot under PID control is shown in
Fig. 6.12(b), where A1 corresponds to the point A in Fig. 6.12(a).
[attachment=29419]
Introduction
The PID Actions
A typical structure of a PID control system is shown in Fig. 6.1, where it can be seen that
in a PID controller, the error signal e(t) is used to generate the proportional, integral, and
derivative actions, with the resulting signals weighted and summed to form the control
signal u(t) applied to the plant model. A mathematical description of the PID controller .
PID Control with Derivative in the Feedback Loop
From Fig. 6.4(b), it can be seen that there exists a jump when t = 0 in the error signal of the
step response. This means that the derivative action may not be desirable in such a control
strategy.
Thus, in practice, the derivative term may be preferred in the feedback path. Since
the output does not change instantaneously for a step input a smoother signal is produced by
taking the derivative of the output. This PID control strategy, which will be denoted PI-D,
is shown in Fig. 6.5.
Recall the typical feedback control structure shown in Fig. 1.2. The controller and
feedback transfer functions can be equivalently written.
Methods for First-Order Plus Dead Time Model Fitting
It can be seen that the model (6.5) is useful for designing a PID controller because of
the availability of a simple formula. The method in Sec. 6.2.1 for finding L and T of a
given plant is simple to use with the graph of a plant step response. Although in modern
computation it is not necessary to reduce a model to this form to find suitable PID controller
parameters, which may be found by using the original model with one of many possible
approaches, nevertheless it can be useful. Given the plant transfer function, we can use
one of the model reduction methods described in Chapter 3. For example, the suboptimal
reduction method [47] is very effective at the expense of an affordable heavy computational
load. The optimal reduced-order model can be obtained with the function opt_app(),
covered in Sec. 3.6. In this section, two other effective and frequently used algorithms will
be introduced.
A Modified Ziegler–Nichols Formula
Consider the Nyquist frequency response shown in Fig. 6.12(a), where for a selected pointA
on the Nyquist plot, the control effects of the P, I, and D terms are shown in the appropriate
directions. Thus, with properly chosen Kp, Ti, and Td, it is possible to move the given point
A on the Nyquist curve of the uncontrolled plant to an arbitrary position on the Nyquist
plot of the controlled system. The typical Nyquist plot under PID control is shown in
Fig. 6.12(b), where A1 corresponds to the point A in Fig. 6.12(a).