Systems of regulation

1) Sistemi of regulation:

They are systems for which the income can think constant or at least variable with one dynamics the much slowest one regarding the constants of time of the system, in the outline to blocks a generator of the largeness of reference with in cascade a ring of feedback having in direct chain the compensator and the process and on the branch of feedback is had the transducer.

 

2) fundamental Performance of an control system:

The stability is fundamental requirement of an control system.

 

3) Causes that can generate errors in an control system :

Being the constant income, the only causes that can give place to errors are disturb and the parametric variations.

 

4) Law of control :

It is the law of the regolator which has like scope that one to concur with the system to work correctly, such law comes normally characterized not for via analytics but for via they experiments.

 

5) industrial Regolator:

Draft of a correction net standard, characterized from a limited number of variable parameters, from which once inserted in a retroazionato process, a law of control in a position to guaranteeing the good operation of the same system is obtained for successive approximations. To the action of the putting in function of the system it needs of a correction net that concurs it to exceed the transitory one.

 

6) Generic mathematical model of an industrial process:

It is characterized from a gain, a delay and or more poles , it can be desumere from the observation of the indiciale answer of a generic process.

 

7) Scope of the insertion of a high gain :

It concurs to reduce the impact on the system of the aleatory member n(t) of the disturbance.

 

8) Meant and scope of the insertion of a pole in the origin :

A pole in the origin is equivalent to an integration in the time and has the task to reduce the infuence on the system of the determinist member of the disturbance that, in the case worse is a step.

 

9) Scope of the insertion of one zero real one :

The reasons are two:

1)       in the case in which the process present 2 poles, the insertion of a pole in the origin that guarantees the astatismo in the comparisons of the determinist member of the disturbance involves that the place present two asymptotes that enter in the skillful semiplan and therefore to growing of the gain k (…necessary in order to reduce the aleatory member of the disturbance) increases the risks of instabilities that can be eliminate to you with the insertion of a zero in how much in the place determine that the asymptote becomes orthogonal to the real axis.

2)       a zero real one corresponds to a derivation in the time and has the task to signal the regolator if the error is diminishing or increasing, if the error stà diminishing, the entity of the correction must be inferior regarding the case in which the error it is increasing.

 

10) Typology of regolators :

to)       action proporzionale P

b)       proportional-derivativa action PD

c)       proportional-integrale action DEVOUT

d)       action proportional-integral-derivativa PID

 

11) Function of transfer of a generic regolator :

One assumes the presence of 2 zeroes and two poles of which one next to the origin and one far away , this last one pu² to simplify itself far away neglecting the pole and carrying the other in the origin obtaining . It is observed that the two functions of transfer have the same harmonic answer in the interest band and that the 2ª introduce of the problems in the comparisons of the harmonicas to vhf which come exalted, becomes therefore necessary to insert various far poles. In the more general shape they have in parallel an action proporziona them, one derivativa and one integral from whose combination the various configurations are obtained.

 

12) Function of transfer of a regolator proporziona them :

often in the applications for this type of regolators instead of the gain coefficient k it comes supplied the band of B proportionality_p in fact if a device not linear place to goes them of the regolator possesses a linear answer in one given band, and to mount of it it increases the gain of the K block_p, diminishes the amplitude of the interval of variation of the escape of the regulation system.

 

13) Function of transfer of a regolator proporziona them more derivativo:

where t_D is the constant of time of the derivativa or constant action of advance payment.

 

14) Function of transfer of a regolator proporziona them more integrativo:

where t it is the constant of time of the integral action, it is observed that being places in parallel the block proporziona them and the integrating block, making the lowest common multiple a stabilizzatrice action is found that this regolator introduces also one zero and therefore.

 

15) Function of transfer of a regolator proporziona more integrating them more derivativo:

it is observed that making the lowest common multiple it is found that this regolator introduces two zeroes and therefore possesses optimal stabilizzatrici property.

 

16) Predisposition of the regolators :

Draft of a procedure that must be realized in order to carry to regimen the system, substantially characterizing the correct values for the constant of K proportionality_p (…or for the band of B proportionality_p), for the integrating constant of time t and for that derivativa t_D .

 

17) Typology of procedures standard for the predisposition of the regolators :

to)       it bases on carrying the system to you closed in feedback to the stability limit

b)       it bases on determining the values to you of the function of transfer of the process

c)       bases to you on the course of the harmonic answer of the process

 

18) First method of Ziegler-Nichols :

The system to the stability limit is a procedure based on carrying, that happens rendering the derivativa action negligible and the integral action placing to minimum t_{the D} and therefore increasing the K gain_p reaches the limit of characterized stability rebelling of a permanent oscillation like answer to whichever sollicitation. The period T_L of the oscillation and the band of B proportionality_p that it has concurred to reach the stability limit concur to predispose in opportune way the regolator through a table realized empirically from Ziegler-Nichols, are had:

to)       for the P regolator one becomes constant and par to -6dB the gain margin

b)       for regolator PD an advance payment of phase to vhf is carried out

c)       for the regolator DEVOUT is carried out a delay of phase to the vlves

the method has the defect that the correction of phase depends on w_-p and not also from the slope of the diagram of the modules.

 

19) According to method of Ziegler-Nichols :

The function of transfer of the process is a procedure based on determining through a measure of the impulsive answer and consequently to plan the regolator, in particular minims must be rendered the derivative and integrating constants of time, and to choose a value whichever for the proportionality constant, in these conditions is placed to us in escape and measure the indiciale answer of the system, considering itself the point of intersection of the tangent in the point of flexed with the axis of the times and the intersection of the same one with the axis of the gain, obtains two values that they are in relation with that present in 1ª the table of Ziegler Nichols in fact intersection with the axis of the times is such that_L = 4 T_m where T_L was the period of the oscillations in 1° the method of Ziegler Nichols, while the intersection with the axis of the amplitudes determines a K_R that it is in relation with the proportionality band.