1. Automatic Control System
II.
Block diagram model

2. Modelling dynamical systems
Engineers use models which are based upon mathematical relationships between two variables.
We can define the mathematical equations:
Measuring the responses of the built process (black model)
Using the basic physical principles (grey model). In order to simplification of mathematical model the small effects are neglected and idealised relationships are assumed.
Developing a new technology or a new construction nowadays it’s very helpful applying computer aided simulation technique.
This technique is very cost effective, because one can create a model from the physical principles without building of process.

3. LTI (Linear Time Invariant) model
The all physical system are non-linear and their parameters change during a long time.
The engineers in practice use the superposition’s method.
x(t)
y(t)
x(j)
y(j)
First One defines the input and output signal range.
In this range if an arbitrary input signal energize the block and the superposition is satisfied and the error smaller than a specified error, than the block is linear.

4. The steady-state characteristics and the dynamic behavior
100
y(t)
WP2
WP1 t
x(t)
100 t
The steady-state characteristic. When the transient’s signals have died a new working point WP2 is defined in the steady-state characteristic.
The dynamic behavior is describe by differential equation or transfer function in frequency domain.

5. Transfer function in frequency domain
Amplitude gain:
Phase shift:

6. The graphical representation of transfer function
The M-α curves: The amplitude gain M(ω) in the frequency domain. In the previous page M(ω) was signed, like A(ω) The phase shift α(ω) in the frequency domain. In the previous page α(ω) was signed, like φ(ω)!
A Nyquist diagram: The transfer function G(jω) is shown on the complex plane.
A Bode diagram: Based on the M-α curves. The frequency is in logaritmic scale and instead of A(ω) amplitude gain is:
A Nichols diagram: The horizontal axis is φ(ω) phase shift and the vertical axis is The a(ω) dB.

7. The basic transfer function
In the time domain is the differential equitation
In the frequency domain is the transfer function

8. Block representation G1 G2 G1G2 G1 G2 G1 G2 G1+G2
Actuating path of signals and variables
One input and one output block represents the context between the
the output and input signals or variables in time or frequency domain
Summing junction
Take-off point (The same signal actuate both path) G1 G2
G1G2 G1 G2 G1 G2
G1+G2

9. P proportional t
Step response Bode diagram

10. I Integral
Step response Bode diagram

11. D differential Step response Bode diagram
The step response is an Dirac delta, which isn’t shown
Step response Bode diagram

12. PT1 first order system
Step response Bode diagram

13. PT2 second order system
Step response Bode diagram

14. PH delay
Step response Bode diagram

15. IT1 integral and first order in cascade
Step response Bode diagram

16. DT1 differential and first order in cascade
Step response Bode diagram

17. PI proportional and integral in parallel
Step response Bode diagram

18. PDT1
Step response Bode diagram

19. Terms of feedback control
controller
plant
controlled variable
compensator or control task
transmitter
manipulated variable
error signal
comparing element
or error detector
actuator
disturbance variable
reference signal
feedback signal
reference input element
action signal
block model of the plant

20. Block diagram manipulation
G1G2 G1
G1+G2 G1 G1 G2 G1 G2 G1 G1 G1 G1 G1

21. Block diagram reduction example