The standardized model equations which are used here originated from the
long history of the Control Theory. These equations represent approaches
towards the description of the real behaviour of dynamic (LTI) systems.
The standardized forms used here are only some of the possible forms. The
reason why they are used here is that they have simple and clear
interpretation. In this context, it is important to note that a
(mathematical) model is always a compromise between simplicity,
precision, accuracy and applicability. Every real system contains, for
instance, noises or nonlinearities if examined enough in detail. In this
light, it might be surprising how many real, important, SISO systems can
be described with these equations.
These standardized model equations can be regarded in a certain sense as
dimensionless. For instance, First order non-integrating system can
describe the dynamic behaviour of the liquid level in a tank as well as
the temperature in an oven. The interpretation of the dimension of the
quantities (including gain!), their normalizing and a choice of the
interval of the simulation are up the user. An important exception is the
“time constants” and the sampling period, which are regarded in seconds.
This is because these quantities have a direct link to the implementation
of the algorithm in a processor.
Discrete – time controllers/regulators often generate a control sequence
u, which is "unconstrained" (large numbers).
Moreover, every real controlled system has physical constraints. It is
difficult to norm the output of the controller (small errors can generate
great responses) when the "exact" description of a controlled system is
unknown or there exist an uncertainty about the exact values of the
system parameters. For this reason the output of the controller is
constrained in the interval 
and 
for unipolar control and for bipolar control,
respectively. The control is then mostly not strictly optimal in the
sense of the time- or of the quadratic optimality. It is, however but
stable and physically realizable.
All the regulators mentioned here are designed for the unit step
as the reference input.
The tuning of the control program on the portal is based on frequency response methods. The Nyquist Plot and Gain and Phase Margins estimating can be employed. It is
expected that the user knows or is able to guess which system they want
to control and how it could vary. The following tuning steps are based on
a direct simulation of the control process and a heuristic assessment of
the results.
In the tab “Requlator design parameters” the user must select
parameters of the controlled system. The controller will be built
with these parameters.
1.There is a rule of thumb that states that
it is suitable to choose Δt between
Ts/4 – Ts/10 for the ZOH.
For the FOH the Δt can be smaller.
2.It is a good idea to select the value of
k so that it is equal or is a multiple of the
largest gain which can occur in the controlled system.
3.Generally, increasing the value of the
sampling period gives rise to the “calming” of the control process.
4.Generally, increasing the value of the gain
gives rise to the “calming” or “smoothing” of the control process.
In the next tab, “Plant modification”, the user can modify the system
being controlled. Here, we can test the influence of a change in the
parameters, including the system order, on the robustness of the control
process. The system will be simulated with those parameters.
5.It is a good idea for k to be set to 1 in
the tab “Plant modification”. The simulation will be then between
or 
, respectively.
[1]Åström. K.J. and B. Wittenmark,
Computer-Controlled Systems: Theory and Design, Prentice-Hall, 1990
[2]Bulut, Yalcin, "Applied Kalman filter
theory" (2011). Civil Engineering Dissertations. Paper 13.
http://hdl.handle.net/2047/d20003550
[3]Kučera V., Algebraic Theory of Discrete
Linear Control, Academia, 1978
[4]Kučera V., Analysis and Design of Discrete
Linear Control Systems, Prentice-Hall, 1991
[5]http://en.wikipedia.org/wiki/Discretization