**Already** noted its structure of the power of electronic device is described by linear differential equation. There for descri

ption of the electrical process in this device may be obtained by solution of the differential equation describing the behaviour of their structure.

The solution of equation is an end time difference table function the equation at all points of reason of definition. There is whole set of such function and the selection of a single one is based on an additional in the form of set initial codition.

1) the general solution of the homogenous differential equation that is the linear differential equation whose right side is zero which describe the properties of of power electronic device.

2) this particular solution which is determined by the properties of the right side and describe the behaviour of power electronic device with the applied disturbance.

For linear equation of first and second order method of solution have been developed. The solution is undertaken in two stage first the homogenous equation and second nonhomogeneous equation.

### Solution of differential equation by Laplace transformation

replacement of operation of difference and shall and integration by the algebraic operations on the Laplace transform in other algebra is a equation Than differential equation.

### Phase trajectories and the point transformation mehtod

Phase plane method permit clear analysis of one-dimensional second order system. In this approach is the behaviour of system is analysis in the spacecraft pointing to a state variable and its daddy weighted. In this case the time variable is eliminated and instead of equation this system is described in the form is point of phase plane. Define by the state variable and its time deliberated corresponding to a single state of system and its known as the first point, image point for respective point the state of change in state in system at its function is known as the face transactor Re. With fixed system parameter only a single phase transactor passes through each point the phase plane Arrow on the face transaction so the displacement of the respectively point our time. The complete set of face transactor constitutes system portrait it provide information of all combination of system parameter and on itself is possible motion the face portrait is expedient for analysis of the motion system in which safe acceleration is possible.

### The primary component method

The primary component method is based on harmony or analysis and takes account of filtering properties of the load fully stocked and periodic function period that the condition in other words that has a infinite number of this continued and continuous derivatives between them may be represented as an infinite to a magnetic series. In view of physical property is the lord to which the periodic function is applied at the filter in other words only transmitter Limited frequency spectrum list of for example if I preconceived pulse voltage is supplied to a DC motor. The inductance of the mature circuit and the moment of inertia for a low-frequency filter for the voltage. Therefore the motor speed will depend only on the main component voltage and the speed pulse due to high frequency spectral components may be disregarded.

In view of filtering properties of power electronic device and the lord we may identify a dominant component in 4 series expansion of a spectrum of periodic discontinuous function,This is known as the primary, is smooth of useful component. All the other component are regarded as noise The Empire the operation of the consuming the system. The motor speed will be depended only the main component of the voltage and this Pitbull pulse due to the high frequency spectral components may be disregarded. In the view of filtering properties Diwali the primary component is assumed by the constant component converter with the DC output first voltage harmony converter with the output by identifying the primary component and by company our attention to the corresponding electrical force we may significantly simplify the analysis of the power electronic device which may be regarded as linear continuous describe the following form the given control plant.

### Stability

Indian analysis and design of power electronic devices stability is primary concern a power electronics by is said to be stable after leaving the equilibrium state under the action of external disturbances its return to that a state where the disturbance is removed. If it does not return to the equilibrium state when the disturbance is removed it is unstable. Normal function of system required at suggestible. Every small change initial condition will produce large error. For linear system the necessary and sufficient condition of stability in that the root of the character cities equation V1 the left half plane of the component. And frequency method parameter determination the system stability without finding the root of the character equation. The method may be used in analysing the device behaviour if it is described in terms of primary component. The necessary and sufficient condition for Linear study dynamic system which level is that all the and diagonal mirror of the positive where you is the order of the characteristic equation.

1) all the cofficinent of the character equation and drank and long the primary diagonal from left beginning with cofficent end of an ending with the free term.

2) from each element of the diagram the corresponding column of the determinant is arranged so that the subscript disc line from top to bottom.

3)the cofficent with below zero subscript on larger and are replaced by zero .

The diagonal mirror is determinant obtained from the illuminating the row and column corresponding to the given diagonal element.

For non linear system stability is determined by mean of the second method which is sufficient stability condition.

According criteria this system is stable if it is possible to select a definite function that include all the system state variable and whose derivative is definite or sign constant but with the opposite sign.

A sign function is function that tends to zero one lead the co-ordinate origin..

Also at the other point of space. If the derivation is sine definite convergence of air is wali the function is selected a quadratic function. Which is by definition assign different positive function is derivative is then analysed if the system is to be a stable the derivative must be signed definite sign constant and negative.

### Control problems and principles

The purpose of power electronic device is to be converted the input electrical energy into output energy with specified character corresponding to needed of the overall system. The actual state of the power electronic device is characteristic by one or more control variable.

In open control the control at the input of power electronic device is calculated on the basic of Technology requirement and complete information regarding not only the power electronic device but also all the disturbance present the controlled variable is advantage of the method is simplicity a significant disadvantage is in need of completely information regarding the power electronic device.

And all the disturbance present at the will need to array in the control variable to eliminate the influence of disturbance on the control process the compensation principle is employed in that case as well as control design Technology requirements with disturbance we also supply control based information regarding the current events is for that disturbance fullstuff the compensation principle is effective if it is possible to obtain information regarding the disturbance.