1.SYNTHESIS OF THE STATE OBSERVER OF COMPLETE ORDER
1.1 Chosing of the object of regulation and its mathematical description in the space of the state
In general the linear system in space of state looks like the following:
1.2 Checking the observability of the object
For a total control it is necessary to have information about the current state of the system i.e values of the variables in every moment of time.Though some variables can be abstract, i.e not have
a physical analogue in the real system, and ,therefore, can not be measured.
Physical initial variables yi(t) are measured and observed in the system if i 1.3Calculation of correction coefficients
The calculation of correction coefficients can be carried out by a method of "balancing coefficients".The essence of this method is in that that u first of all should make a description of the system using state space
equations.
Then, after defining matrices A, B, C and D, and checking up the system on observability we find the characteristic polynomial of the state observer using the formula:φc(p)= p+l
Observing devices which restore the variables of an object can also identify the parameters of an object that can not be measured.In this case observing devices are made with selfregulation after parameters that are identified through the introduction of integrators, input signals of which is the difference between measured and estimated values of the variables of an object.
2.1 Adaptation to the change of the moment of inertia of billow of engine
We will consider the application of adaptive observing device of identification in the system of the inferior adjusting of speed of the engine of direct current.Unplanned changes of the moment of inertia appear in electric drive.We will build the adaptive observing device identifying changing of the moment of inertia.To simplify we will assume that in a closed system ,according to EDS, the feedback can be neglected, and the moment of resistance remains the same.
As the main action directed on the nonsteady part of the object we will take the current of the engine, and as an output coordinate we will take the speed.The scheme of adaptive system with observing device made in Simulink environment of Matlab package is represented on illustration 2.1
2.2 Adaptation to the change of active resistance of the engine
In the process of work of the electric drive(ED) systems there is a change of parameters of the object of regulation under the influence of the thermal state of the engine and modes of it's operation.It can result in violation of system characteristics and even loss of system efficiency. Therefore, nowadays the development and realization of devices that allow to adapt the system of regulation to change of parameters of the object of regulation is so relevant.
The structural diagram of SO model which restores the value of active resistance is shown on the illustration 1, where the following denotations are used:
KТ, KС -coefficients of feedbacks according to the current regulated and speed:
Km, Tm- amplification factor and equivalent time constant of energy converter which;
L a – inductance of electromagnetic circle of engine;
L1, L2 - coefficients of basic corrective feedback of SO which can be found with the help of the formula:
On the basis of these researches can be made a general conclusion that a state observer performs functions were entrusted to it, therefore, it can be recommended for use.
is completelely observed if there is such a moment tk>t0that the initial state of the system X(T0)=X0can be defined if u know the value of Y(t) in a definite interval of time
[tk...t0] .
But it is assumed that tkis any not given interval of time that can be in case tk>t0 .
If the matrixes A and C are respectively [n*n] i [r*n] then A and C are observable in case the system(2.1) is totally observable. Then we have the criterion of observability:it is necessary for the matrix observed
with the value n*[r*n] to have rank n .only then a linear stationary system can be considered completely observed.
2.2.SYNTHESIS OF KNOT OF ADAPTATION
Ra – calculated (approximate) value of active resistance of engine;; Tl=La/Ra – calculated value of electromagnetic time constant;;
γ– multiplicity of mean geometric value of the root
Ω0=γ /Tµ which depends on a kind of the desired characteristical polynomial of the system (for example, if as the desired the polynomial of Batterworth of 2 order is chosen then , γ=1,414);
α β – correction coefficients of channel of identification with the value opposite to Ra .
The choice of correction coefficients α β was made on the basis of several sessions of mathematical modeling during which it was found out that the value of the coefficient b plays the main role in the identification of active resistance .The graph of transitional processes with the parallel work of the system of regulation of speed of engine of direct current П-52 (59 кВт, 220 V, 580 об/хв.) and observer work is shown on the illustration 2.3.Analysis of the graphes showed that an appropriate value of β is 80...120.
Литература