d system, check whether the system is stable or not using Niquist, Hurwitz criterions and sufficient condition of stability, calculate eigenvalues ​​and-norms of the uncompensated and compensated system. We will also synthesize the real PD-compensator () which would guarantee desired phase margin at gain crossover frequency and then will draw the conclusions. br/>
1. Initial data for the term paper performance
. 1. Control system of nuclear reactor rods position
Table 1. Individual variants for control system of nuclear reactor rods position
No,/sec,
deg62 0.124.4 360
2. Calculations
I. Analyze of uncompensated system
) Calculation of the transfer function of the whole uncompensated system :) without Matlab
Theoretical information:
A transfer function of the analog system is the ratio of the Laplace transform of the output signal to the Laplace transform of the input one under zero initial conditions. A continuous time SISO (single-input-single-output) transfer function is characterized by its numerator and denominator, both polynomials of the Laplace variable. p> Calculations:
The control system of nuclear reactor rods position looks like:
. 2
В
So, the transfer function of open-loop uncompensated system is:
В В
And the transfer function of closed-loop uncompensated system is:
В В
b) with Matlab
Program code:
disp ('Task 1. Analyze of uncompensated system')
= tf ([5]); = tf ([6], [1 6 0]); = tf ([0.2]); = tf ([10.5]); = tf ([ 1], [0.1 1]);
= series (W1, W2); = series (W12, W3);
('Transfer function of open-loop uncompensated system is') = series (W123, W4) ('Transfer function of closed loop uncompensated system is') = feedback (Wolun, W5, - 1) % task 1.1
Results of the program:
Task 1. Analyze of uncompensated systemfunction of open-loop uncompensated system isfunction:
^ 2 + 6 sfunction of closed loop uncompensated system isfunction:
.3 s + 63
.1 s ^ 3 + 1.6 s ^ 2 + 6 s + 63
2) define zeroes and poles of obtained transfer function
