Engineering Systems Modelling And Simulations Assignment Sample
1.0 Introduction
The differential equations are the baseline of all the electrical calculations of the engineering systems and these methods are used for the design and development of the Matlab system. This can be addressed that there is a huge ideology that is regarding the changes related to the development of the ODEs and their theorems. The changes in the subject are the main idea regarding the theorems of ordinary differential equations that are used for developing the rocket launching and proper calculation of the design. Hence proper addressing of the facts says that there is a huge development of the systems regarding the design associated with the development of various ideas regarding the development of the design.
The project is regarding the developments in the facts that are regarding the changes in the ordinary differential equation. The changes in the system are based on the structure that is related to the ODE and differentiability of the design is based on the data that is required for the design and development of the MATLAB coding and the design of the simulation is also provided in the system and thus the overall development is also provided in the system simulation.
2.0 Matlab Simulink Model
2.1 MATLAB analysis
The MATLAB model is also designed and hence this can be said that the differential equations can be easily divided in the Matlab simulation and design of the circuit. The development of the models is provided in the basement of the system and this can be more like the Simulink model that is the block diagram regarding the developments in the data and overall ideology. Hence the ideology can be properly addressed which shows that there are various ideas showing the development in the design and changes of the system.
MATLAB is software that shows various ideas that are related to the simulation of the system. That is the system is based on the aftereffect of the ideas that are related to the design and development of the structure. Hence this can be seen that MATLAB is a software that can show the engineers the fault in the design and development that are related to the ordinary differential equation. Hence this can be said that there are various utilities of the software and hence this can be used for the development of the various aspects of the ordinary differential equation and design of the circuit.
MATLAB is such software that has the changes in the overall design changes that can be implemented in the overall development associated with the new innovation and design in the coding and development. Hence this can be said that there are various utilities that are related to the development of the subject matter and the design of the ODE. ODE can be used for the development of the various ideas that are related to engineering mathematics and the Laplace transform. The ODE can be developed according to the changes that are required in the Matlab development of the structure.
3. Ordinary differential equation
3.1 ODE 45 and ODE 23
The initial values of the x0 and y0 are selected and they are 2 and 4 and the final value of x is 10. The step size is h=0.01 and the counter is selected as k=1. The initial starting of the computation shows that x1=x0 and y1=y0 and the for loop then starts. The for loop shows that there are x=x0:h:x that is the loop starts through the difference of various ideas regarding the changes in the structural analysis of the system. Hence this can be said that there are various ideas that are regarding the changes in the system of ODE.
Figure 1: Matlab Coding
(Source: Self-created in MATLAB)
The output of the equation is related to the development of the calculation of the system and the ODE calculation is also provided where the output shows that the x=12 and y=-3 and this starts from the t=0 and x=0. The changes in the structural analysis are based on the values and system developments regarding the changes in the overall development. The ODE 45 and ODE 23 are also included in the system and the calculation is also based on the facts that are provided in the system of structure. Hence this can be said that there are various formulations related to the development of the structure related to the development of the ODE.
Figure 2: The final result of the MATLAB coding
(Source: Self-created in MATLAB)
The changes in the structural analysis are also provided in the system and hence this can be said that there are various ideas that deal with the structural analysis of the system. This can be said that there are developments in the overall structure related to the development of system analysis. Hence this is evident that the MATLAB software is needed for the development of the structural analysis of the system that can have an overall change in the system. The structural analysis of the ODE is required for the development of the structural analysis of the system required for the ODE and its system.
The Runge-Kutta methods are used for the development of the formulas that are provided in the system. The changes in the ODE are huge and hence this can be said that there are various developments that are related to the development of the system. The t^4 is the additional value of the system and hence this can be said that the ODE is based on the system generation and proper coding in MATLAB. Hence addressing the facts shows that coding is important for system development and analysis. The overall design of the system shows that there are developments regarding the ODE structure.
Figure 3: Control diagram of ODE circuit diagram
(Source: Self-created in MATLAB)
The control diagram of the system shows that the source consists of three ports that are from the 1 transom under and the other two form the or gates of 2 and 5. The overall development of the modelling shows that the graph is regarding the changes that are needed for the proper ideology. The Laplace transform is also provided in the structural analysis of the circuit and the overall development of the system. Hence this can be said that there are various developments of the system regarding the changes in the structural analysis of the system.
Figure 4: The output graph of the system circuit
(Source: Self-created in MATLAB)
The output of the graph shows that the graph is related to the stepwise response regarding the developments that occur in the scope. The overall changes of the system are based on changes that can be initiated with the changes in the system and hence this can be said that the overall development is based on the structural analysis of the circuit. Hence this can be said that there is a huge development regarding the changes that can be implemented in the system and the graph becomes streamlined after some time of the propagation of the wave.
Figure 5: The coding related to the ODE generation
(Source: Self-created in MATLAB)
The coding shows that there are various developments in the system of ODE and hence this can be said that there are 4 digits that are selected. The ‘syms’ are selected as x(t) and Dx=diff(x,t) and D2x=diff(x,t,2) and this show the proper values that are selected for the change of the system. The changes in the structural analysis are based on the values and system developments for the coding and design. The ODE 45 and ODE 23 are also included in the system and the calculation is also based on the facts that are provided in the system of structure.
Figure 6: Output of the ODE coding
(Source: Self-created in MATLAB)
The output shows that there is the proper solution for x that solves the proper solution regarding xSol(t) and the output is shown as, 0.1111*exp(-5.0*t)-0.2778*exp(-2.0*t)+0.1667. That is the system is based on the aftereffect of the ideas that are related to the design and development of the structure. Hence this can be seen that MATLAB is software that can show the engineers the fault in the design and development that are related to the ordinary differential equation. Hence this can be said that there are various utilities of the software and hence this can be used for the development of the various aspects of the ordinary differential equation and design of the circuit. MATLAB is such software that has the changes in the system regarding coding and development of the system that can be implemented in the overall changes regarding the coding and development. This can be addressed that there are various utilities that are related to the development of the subject matter and the design of the ODE.
The overall calculation is based on the collection of the values that are connected with the ODE equation. The overall requirement is based on culturing the overall solvation techniques regarding the changes in the ODE calculation. Hence this can be said that the ODE calculation is based on the structural analysis of the equation.
3.2 Van Der Pol oscillator
The Van Der Pol oscillator is a device that captures the damped vibrations so that the vibrations can be easily understood and hence this can be said that the oscillator is utilized for the development of various damped vibrations studies. The energy measurement is also a part of the system because the energy is stored in the form of damped vibrations. These vibrations are properly processed and the main outcome is based on the facts that are required for the development of the overall outcome. The Van Der Pol equation is followed by this oscillator and these oscillations are gathered by the change in the energy regarding the damped vibrations in the system (Chen et al., 2018). The oscillator is properly engaged in initiating the photons that are required for the measurement of the energy that is gathered from the changes in the vibration wave. Hence this can be said that there are various ideas related to the Van Der Pol oscillator and its functions related to the energy measurement and development of the damped vibrations.
Figure 7: Van Der Pol coding
(Source: Self-Created in Matlab)
The function that is selected is the Van Der Pol function and the stats are also provided along with tspan. The tspan= [0 300] and y0= [2 0] because the time span is selected between 0 to 300 seconds and the final position is 2 inches from 0. The displacement is also provided in the stats that are provided for the solvation of ODEs. The displacement is recorded in the form of time ‘tics’ and the time is t2 and the final position is y2 (DABWAN and HASAN, 2020). The plotting is done for the displacement of the system and the overall wave generation is also provided that can prove the overall development of the system of coding. The plotting is done in three dimensional way and the subplot position is (2, 2, 1) along with the change in the subplot position that is in sequence.
Figure 8: Output plot of Van Der Pol oscillations
(Source: Self-Created in Matlab)
The plotting shows the changes in the system subplot positions in a proper sequence that is (2,2,1), (2,2,2) and so on. The overall figure shows that there are multiple oscillations in one position and the overall graph is moving up and down according to the proper oscillation curve. Hence this can be said that the Vander poll model of oscillations is totally dependent on the system oscillations (Madni et al., 2019). The overall solvation shows the behaviour of the Van Der Pol oscillations regarding the changes in various energy requirements. Hence this can be said that there are various ideas related to the Van Der Pol equations and oscillations.
Figure 9: Calculations of Van Der Pol oscillators
(Source: Self-Created in Matlab)
The above picture shows the calculation regarding the Van Der Pol oscillations.
Figure 10: Control diagram of Van Der Pol oscillators
(Source: Self-Created in Matlab)
This diagram shows the overall design of the control diagram related to the Van Der Pol oscillators.
Figure 11: Step response of Van Der Pol oscillators
(Source: Self-Created in Matlab)
3.3 High pass and low pass stages
The plot that is provided here is the bode plot and this portrays the overall idea regarding the switching frequency of the filter. There are two types of filters and they are high pass and low pass filters. The high pass filters and the low pass filters have the program for the transfer of the signal from proper AC to rectified DC and this utilizes capacitors in the field (Schluse et al., 2018). The capacitor that is used is for high impedance and these high impedances are functional at certain frequencies. Hence this can be said that there are high pass and low pass filters are utilized for the maintenance of the rectified current.
Figure 12: Control diagram of HP stage
(Source: Self-Created in Matlab)
The control diagram shows that there are enough ideas that can be applied to the design.
Figure 13: Output response of HP stage
(Source: Self-Created in Matlab)
The figure shows the output response of the HP stage.
Figure 14: Cut-off frequencies for the HP stage Bode diagram
(Source: Self-Created in Matlab)
The figure shows the frequencies for the HP bode diagram that is regarding the cut off stage.
Figure 15: Control diagram of LP stage
(Source: Self-Created in Matlab)
The figure shows the control diagram of the LP stage of the system
Figure 16: Output of the control diagram
(Source: Self-Created in Matlab)
The output of the control diagram is shown in the following figure.
Figure 17: Bode diagram
(Source: Self-Created in Matlab)
4. Methods for determination of a transfer function
There are various ways for the proper determination of the transfer functions and they are,
Data flow diagrams: The data flow diagrams are plots and graphs that show a proper design regarding a flowchart. Another compression of the data flow chart produces the monitoring of the management and this can be a proper convolution of the transfer functions (Lim et al., 2020). The technology that employs the change in the structural transfer function is the LTI technology and this technology is based on the structural analysis of the system. This can be said of the LTI technology as the basement of the system analysis of the transfer function.
Another method for the determination of transfer functions are block diagram techniques and this includes the control diagram of the system. The control diagram of the system is based on the facts that are related to the power diagram of the system (Rosique et al., 2019). The block diagram contains the different ideas regarding the changes that are included in the power diagram. Hence this can be said that the overall ideology of transfer function is based on the block diagram technique.
5. Conclusion
The study of the topic provides exclusive coding ideas regarding the ODE and their proper sensing of the structure. This can be more and more ideal regarding the proper study regarding the facts that are collected by the researchers. The overall figure shows that there are multiple oscillations in one position and the overall graph is moving up and down according to the proper oscillation curve. Hence this can be said that the Vander poll model of oscillations is totally dependent on the system oscillations. The overall solvation shows the behaviour of the Van Der Pol oscillations regarding the changes in various energy requirements.
Reference list
Journals
Ab du Al-Rabahi, Z.A. and Hasan, Y.Q., 2020. New Modified Adomin Decomp osition Metho d for Boundary Value Problems of Higher-order Ordinary Differential Equation. Asian Research Journal of Mathematics, pp.20-37.
Bai, M., Choy, S.T., Zhang, J. and Gao, J., 2021. Neural Ordinary Differential Equation Model for Evolutionary Subspace Clustering and Its Applications. arXiv preprint arXiv:2107.10484.
Bocquet, M., Brajard, J., Carrassi, A. and Bertino, L., 2019. Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models. Nonlinear Processes in Geophysics, 26(3), pp.143-162.
Chen, R.T., Rubanova, Y., Bettencourt, J. and Duvenaud, D., 2018. Neural ordinary differential equations. arXiv preprint arXiv:1806.07366.
DABWAN, N.M. and HASAN, Y.Q., 2020. Solving Second Order Ordinary Differential Equation Using a New Modified Adomian Method. AMSJ, 9(3), pp.937-943.
Fröhlich, F., Loos, C. and Hasenauer, J., 2019. Scalable inference of ordinary differential equation models of biochemical processes. Gene Regulatory Networks, pp.385-422.
Gotoh, H. and Khayyer, A., 2018. On the state-of-the-art of particle methods for coastal and ocean engineering. Coastal Engineering Journal, 60(1), pp.79-103.
Ilchmann, A., Leben, L., Witschel, J. and Worthmann, K., 2019. Optimal control of differential‐algebraic equations from an ordinary differential equation perspective. Optimal Control Applications and Methods, 40(2), pp.351-366.
Khan, A.T. and Naher, H., 2018. Solitons and periodic solutions of the fisher equation with nonlinear ordinary differential equation as auxiliary equation. American Journal of Applied Mathematics and Statistics, 6(6), pp.244-252.
Lim, K.Y.H., Zheng, P. and Chen, C.H., 2020. A state-of-the-art survey of Digital Twin: techniques, engineering product lifecycle management and business innovation perspectives. Journal of Intelligent Manufacturing, 31(6), pp.1313-1337.
Madni, A.M., Madni, C.C. and Lucero, S.D., 2019. Leveraging digital twin technology in model-based systems engineering. Systems, 7(1), p.7.
Mohanty, M. and Jena, S.R., 2018. Differential transformation method (DTM) for approximate solution of ordinary differential equation (ODE). Journal homepage: http://iieta. org/Journals/AMA/AMA_B, 61(3), pp.135-138.
Rosique, F., Navarro, P.J., Fernández, C. and Padilla, A., 2019. A systematic review of perception system and simulators for autonomous vehicles research. Sensors, 19(3), p.648.
Schluse, M., Priggemeyer, M., Atorf, L. and Rossmann, J., 2018. Experimentable digital twins—Streamlining simulation-based systems engineering for industry 4.0. IEEE Transactions on industrial informatics, 14(4), pp.1722-1731.
Wang, P., Wu, P., Wang, J., Chi, H.L. and Wang, X., 2018. A critical review of the use of virtual reality in construction engineering education and training. International journal of environmental research and public health, 15(6), p.1204.
Weber, F., Theers, S., Surmann, D., Ligges, U. and Weihs, C., 2018. Sensitivity analysis of ordinary differential equation models.
Yang, J., Gimeno, J. and la Llave, R.D., 2021. Parameterization method for state-dependent delay perturbation of an ordinary differential equation. SIAM Journal on Mathematical Analysis, 53(4), pp.4031-4067.
Zhang, T., Yin, Q., Caffo, B., Sun, Y. and Boatman-Reich, D., 2017. Bayesian inference of high-dimensional, cluster-structured ordinary differential equation models with applications to brain connectivity studies. The Annals of Applied Statistics, 11(2), pp.868-897.
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