Lecture 1.6. We use the substitution:
We use the substitution: 
(6.25)
We may transform Eq.(6.25) to the following form:
(6.26)
where:
- a real component of the system frequency transfer function;
- an imaginary component of the system frequency transfer function;
(6.27)
According to Eq.( 6.28) we have:
(6.42)
where:
- the module of the frequency transfer function
- the argument or phase of the frequency transfer function
- real and imaginary components of frequency transfer function.
Using our example – Eq.(6.34), we may define the system module and argument of the frequency transfer function:
(6.43)
(6.44)
(6.45)
(6.46)
Gain-phase frequency characteristic (the Nyquist diagram) – is the frequency locus of tips of the vectors which correspond to the system frequency transfer function 
while circular frequency 
is changing from 0 to 
:
- values of are plotted on real axis (abscissa axis, X-line);
- values of 
are plotted on imaginary axis (ordinate axis , Y-line);
- for each 
value we plot a separate point according to corresponding values of 
and 
;
- the obtained points are the system gain-phase frequency characteristic.
Gain-phase frequency characteristic may be constructed for positive as well as negative values.
The change in sign will result in conjugate gain-phase frequency characteristic (which is shown using the dashed line).
The essence of positive and negative frequencies may be explained using the Fourier transform:
(6.46)
Using the Fourier transform we may convert 
time function into 
frequency function.
It means that the time function is represented by an infinite sum of vectors with infinitesimal amplitudes and various circular frequencies which are rotating in the complex S-plane.
This sum may be defined using the inverse Fourier transform:
(6.47)
where 
is the absolute convergence abscissa.
Fig.6.2 The system gain-phase frequency characteristic (Nyquist diagram)
№17
17.2 Explain the construction of static load characteristics (load characteristic).- Lecture 2.9.
17.3 Define the control system’s static transfer function if 
Since the denominator contains s variable, then on condition that 
.
Thus, the equivalent transfer function is equal to zero.
№18
№19
19.2 Define the equations of the Nyquist stability criterion in order to define the stability of the following control system.
During the 1st step you have to define the open-loop transfer function:
This case referred to the function 
( 
> 
) (Tabble 9.6 in: R.C.Dorf, R.H.Bishop. Modern control systems. 11th edition. Addison-Wesley. 2008.)
19.3 Define which Nyquist diagram corresponds to an amplification link
