DESCRIPTION:
Field Of Invention
The invention presented in the paper refers to generate ripple free dc output regardless for any MIMO Nonlinear system and the control techniques ensure excellent static and dynamic performances, alsoresulting in simple control implementation by optimal LQR controller.
Background of Invention
DC-DC converters are widely used in dc motor drives, computer systems and communication equipment's, position control systems,photovoltaic and fuel cell application.The efficient proposed developed DC-DC converter is Luo converter it overcomes to parasitic problems present in the classical dc-dc converter. The harmonics Levels present in Luo converter is less compared to the classical buck converter. The time variations and switching nature of the power converters were non-linear.
The various control techniques applied for both transient and steady state regions of that particular converter. The invention Optimal LQR isa very easy process to analyse the servo and Regulatory response of any MIMO system for both steady state and Dynamic region.A relative assessment of the Proportional- Integral (PI) Controller. Model Predictive Controller (MPC) and Linear Quadratic Regulator (LQR) are used for the nonlinear plant.
The PI control has been presented to control of switching power conveners. The PI control is designed to the specifying desired nominal operating point for Luo Convener, then regulating Luo Converter are closer to the nominal operating point in the case of sudden disturbances, set point variation, noise, modelling errors and the components variations. In control theory it is sometimes possible to linearize the nonlinear systems and apply linear techniques. Model Predictive Control (MPC)can more explicitly take into account constraints on the signals in the system, which is an important feature in many industrial processes. However, the "optimal control" structure in MPC is only a means to achieve such a result, as it does not optimize a true performance index of the closed-loop control.
The theory of optimal control is concerned with operating adynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. The settings of a controller governing either a plant or process are found by using a mathematical algorithm that minimizes a cost function with weighting factors supplied by a , engineer. The cost function is often defined as a sum of the deviations of key measurements from their desired values. The algorithm thus finds those controller settings that minimize undesired deviations. The magnitude of the control action itself may also be included in the cost function.
The LQR algorithm reduces the amount of work done by the control systems engineer to optimize the controller. However, the engineer still needs to specify the cost function parameters, and compare the results with the specified design goals. Often this means that controller construction will be an iterative process in which the engineer judges the "optimal" controllers produced through simulation and then adjusts the parameters to produce a controller more consistent with design goals.

Brief Description of the Figures
A brief description of the figures is given below to get a better understanding of the work presented.
Fig. 1.Displays the circuit diagram of Luo converter
Fig.2shows the mode 1 operation of the Luo converter
Fig.3 represents the mode 2 operation of the Luo converter
Fig.4. demonstrations the block diagram of Luo converter using PI controller
Fig.5. shows the block diagram of a model predictive control system
Fig.6.displays the block diagram of Luo converter using model predictive control
Fig.7.shows the block diagram of LQR
Fig.8.illustrates the block diagram of Luo converter using LQR
Fig.9.shows step response for PI,MPC,LQR control of Luo converter
Fig. 10.shows servo response for proposed Luo converter at 10 sec for various controllers
Fig. 1 1 .shows regulatory response for line disturbance at 10 sec for proposed Luoconverter
Fig. 12.shows regulatory response for loaddisturbanceat 10 sec for proposed Luoconverter
Fig. 13.shows performance evaluation of Luo Converter for PL MPC.LQR.
Detailed Description Of The Invention:
The whole invention is illustrated in form the block diagram of Luo convener using Pl.MPC &LQR controller. The block diagram is explained in detail which follows now.
I. Mathematical Model of Luo Converter
To obtain the mathematical model of theLuo convener, the state model of the converter is derived by two modes of operation. When S=I.MOSFET switch conduction sub interval and S=0 diode conduction sub interval.
The convener dynamics is derived by using state space averaging method.The averaged system matrix can also be formulated for the converter by introducine a duty ratio c.
a. For mode 1 operation
When switch is ON inductor L| is charged for supply voltage E. The same time, the inductor L2 absorbs the energy source from capacitor C\. The capacitor C2load is supplied to the load.

b. For mode 2 operation
During switch is in OFF state, and hence, the current is drawn from the source becomes zero. Current L| flows through freewheeling diode to charge for capacitor C|. Current L2 flows into C2 -R circuit and the freewheeling diode D to keep itself continuous.
All state variables are subscribed as* ;s and all sources are subscribed u:s then the state space representation of the system as follows as
The transfer function is given by

II. DESIGN OF PI CONTROLLER FOR POELC
For optimizing the stability of the positive output elementary Luo converter a PI control is a more feasible approach. The PI control has been presented to control the switching of power conveners.
The PI controller settings are proportional gain (Kp) and integral time (T,-). designed by Zeigler - Nichols tuning technique. Ziegler and Nichols suggested to set the values of Kp= 0.25and T,= 0.016s. The optimal setting values of PI Controller (Kp and Tj) for Luo Converter are obtained by the minimum values of Integral Time Absolute of Error (1TAE). Integral Time Square of Error (ITSE). Error in output voltage and change in the duty cycle of the power switch is respectively with input and output of the PI controller.
Ill DESIGN OF MODEL PREDICTIVE CONTROLLER FOR POELC
Model Predictive Control (MPC) is an ideal control system based on numerical optimization. The future control sources and future plant responses are predicted by utilizing a system model. A process model can predict the current values of the output variables. The differences between the actual and predicted outputs, serve as the feedback signal to a Prediction block. The predictions are used in two types of MPC calculations, which are performed at each sampling instant the control calculationsand the set-point calculations.

For equality constraints on the input and output variables, the upper and lower limits can be included in either type of calculation. The MPC configuration is similar to both Smith predictor configuration and internal model control configuration .The model acts in parallel with the process and the residual serves as a feedback signal. MPC has more impact on industrial practice. Typical optimization objectives include maximizing a profit function, and minimizing a cost function, the optimum values of set points change frequently due to thevarying process conditions. The constraint changes are due to variations in process conditions, equipment, and instrumentation, In MPC the set points are calculated each time of the control calculations. The MPC calculations are based on the current measurements and predictions of the future values of the outputs. The actual output is v; the predicted output is u for S!SO control is shown. At the current sampling instant, denoted by k, the MPC strategy calculates a set of M values of the input {u(k +i - 1). i = 1. 2. . . M}.
IV. DESIGN OF LQR FOR POELC
LQR control method is used to improve the convener response. The LQR involves the choosing of positive definite state and control input matrices O and R. which provide satisfactory closed-loop performance. The closed-loop Eigen values were related to these weighting matrices. .Many methods arc available for determining weighting matrices, with the closed-loop poles placed in a specified region of the complex plane. A sequential procedure which selects the weighting matrix O and degree of relative stability to position individually and arbitrarily the real parts of the Eigen values of the optimal LQR system has been presented.
A sequential method uses the classical root-locus techniques has been developed for determining the weighting matrices in the frequency domain to retain closed-loop Eigen values in a desired region in the complex plane, but the main method is based on trial and error, although time consuming. In this method, the feedback gain matrix is determined if J energy function is optimized. To achieve equilibrium among range control parameters, response speed, settling time, and proper overshoot rate, all of which guarantee system stability, the LQR is employed.
The system is in the form x(t) = Ax(t) + Bu{t)
The LQR method determines the K matrix of the equationu(t) = —Kx{t)
..E*.. For continuous.time system,.1^.&.eaergy_&nctionJ«= ,L &xT Qx +AuTjhi)A<\% .

Output matrix C denotes that ,v2&*4 are accountable for the servo response of the system. So that the optimal gain matrixes Ki and K4 are connected through feed forward for the systemwhereas the regulatory response is controlled b\a1&jr3. The corresponding gain matrixes K\ and K* are connected as feedback for the system.
Matrices R and Q express the relationship between error and energy expense rate. R and Q are the positive matrices is given by
In addition to the state-feedback gain 1C, LQR returns the solution s of the associated Riccati equation
ATS + SA - SBR~lBrS + Q = 0
Optimal gain K, solution of Riccati equation S are determined by,
— ..

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CLAIMS
1. We claim the Luo converter is designed using PI controller
2. We claim the Luo converter is designed using Model Predictive Controller
3. We claim the Luo converter is designed using LQR Controller
4. We claim the simulation results confirm that PI controller gives smooth servo response in term of initial overshoot.
5. We claim the Proposed MPC rejects the line disturbances and it gives uniform servo response with very high peak overshoot.
6. We claim the results proved that LQR controller gives the smooth response for Servo response as well as Regulatory response.
7. We claim the desired voltage with reduced 1AE, 1TAE. !n this method stable and ripple free output is obtained.
8. We claim the simulation results that are verified using design and calculations.
9. We claim dc-dc Luo conveners are suitable and convenient to be applied to the fuel cell applications with low ripples.
1 Q^W'e claim the optimal LQR controller for any type of SISO and MIMO systems. lOcbJVe claim the optimal LQR controller for linear and nonlinear systems. !0£>V'e claim the optimal LQR controller for any frequency of operation.