State-Space Interpretation; Opening The Pole Place Window; Manipulating The Closed-Loop Poles; Time And Frequency Scaling - National Instruments Xmath Interactive Control Design Module ICDM User Manual

State-Space Interpretation

Opening the Pole Place Window

Manipulating the Closed-Loop Poles

Time and Frequency Scaling

© National Instruments Corporation
In a state-space framework, it is common to classify the closed-loop poles
as n "control eigenvalues" and n "estimator eigenvalues." But, in fact, it
makes no difference in the final controller transfer function how you
classify the closed-loop poles.
In other words, in a state-space framework, swapping a "control
eigenvalue" and an "estimator eigenvalue" will result in different feedback
and estimator gains, but the same final controller.
The Pole Place window can accept any controller with n poles, or n + 1
poles provided the controller has at least one pole at s = 0. The Integral
Action toggle button will be properly set. In particular, it accepts all LQG
and H controllers. This allows the user to manually tune the closed-loop
poles in a design that was, originally, LQG or H . In this case, you cannot
read the resulting controller back into the LQG or window since the
controller no longer has this special form.
The closed-loop poles and zeros can be dragged and edited interactively.
Refer to the Graphically Manipulating Poles and Zeros
Chapter 2, Introduction to SISO
manipulating poles graphically.
The slider and variable-edit box show the average value of the closed-loop
pole magnitudes, and therefore can be interpreted as, roughly, the
bandwidth of the closed-loop system. The average frequency is given by:
where , ..., are the closed-loop poles. Notice that the average is
1 2n
geometric.
You can change F by dragging the slider or typing into the variable edit
avg
box. The effect is that the closed-loop poles are all multiplied by a scale
factor in such a way that becomes the requested value. Therefore, by
changing F , you are time- or frequency-scaling the closed-loop
avg
dynamics.
Design, for a general discussion of
F =
avg 1 2 2n
6-5 Xmath Interactive Control Design Module
Chapter 6 Pole Place Synthesis
section of
1/2n