J. Furze, Q. Zhu (2014) Orthogonal relations coupling renewable energy and sustainable plant systems. 6th ICMIC, Melbourne, Australia

Orthogonal Relations Coupling Renewable Energy and Sustainable

Plant Systems

James Furze and Quanmin Zhu

Faculty of Environment and Technology

University of the West of England

Frenchay Campus, Coldharbour Lane

Bristol, BS16 1QY, UK

Presented in 2014 at 6th International Conference on Modelling, Identification and Control, Melbourne, Australia, 3-5th December ©

Introduction / background

• Block (systems) approach for Plant Systems and Renewable Energy Grids as may beapplied to sustainable urban agricultural systems:

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• Previously we have shown the control strategy used in characterisation of plantsystems, following the use of the dimensions of life-history based strategyenvironments; plant metabolism and life-forms which have been shown on a globalscale [1], [2]. These characteristics show discrete distribution patterns according tothe water-energy dynamic present on a global scale.

• Renewable energy systems planning is also subject to discrete distributionaccording to the variables of energy (solar flux) and wind (easterly wind), presenton a global scale.

• Implementation of MOGA approaches for dispersal of each system block and combinatorial T-S-K Fuzzy-MOGA-Lyapunov stability identifies convergence between the two blocks in order that effective PSS can be formed.


Plant System (contained, urban agriculture)

Renewable Energy System (Solar; Wind)

Planning Support System (PSS)

Data used to construct the frameworks for Adaptive Neuro Fuzzy Inference System Blocks for Plant Systems.


Plant environmental data of the most extreme environment of E7, a candidate CrassulaceanAcid Metabolism environment (the Sudan), is sourced from the Intergovernmental Panel on Climate Change [3]. Temperature is designated A1; Precipitation is designated A2. The data used is that in the time frame 1960-90 of use in current plant characterisation modelling [4].

Framework of climatic data used in implementation of wind and solar renewable energy ANFIS


Climatic data of easterly wind and solar flux is sourced from the Intergovernmental Panel

on Climate Change. Data is processed with Matlab (Version R2010a©), shown at 20km

resolution in the projected time frame 2011-2030 (following stochastic weather

generators and scenario of the IPCC[5]). Figure 3 data is designated A3; Figure 4 data is

designated A4. Data are quantified according to Table I.

Algorithms for System Blocking and T-S-K Nodal Structure


The algorithmic framework for blocking of plant systems has been previously covered [2], the following T-S-K statement is made for E7 Crassulacean Acid Metabolism plant species:

The above algorithm represents the first block expanded using MOGA in slide 9, Figure 7

Efficient, T-S-K algorithmsare given representingthe projected conditions(Figures 3 and 4); the dataresults from stochasticweather generatorsdeveloped by the IPCCand are consistent withprojective models,GATOR-GCMOM [6].

T-S-K algorithmic detail of system blocks for Renewable Energy


Equation (2) represents the conditional statement for wind and solar renewable systemsimplementation (Future Renewable Energy (FE(REN)) across January 2011-2030, given as anexample of the rule base which is expanded in Figure 5, the full nodal structure represents allfour sets of data for the renewable energy system block across an annual period. The ANFISnodal diagram of Figure 5 represents ¼ of the 2011-2030 mean period for the variables, as suchit is akin to a type-2 fuzzy system [7] within the block constructed for FE(REN).

T-S-K Nodal Structure- the ‘Engine’ for the Renewable Energy Block


Simplified ANFIS modelstructure of Global FutureSolar and Wind Energyinstallations.

Equation (2) Expands into 34rules in Figure 5. The use ofdiscrete-time slices provideslogical reasoning forapplication of Lyapunovprinciples / sliding systems [8],[9].

Discrete/stochastic relationsare seen when consideringeach longitudinal bandconsidered within thealgorithm, consistent withpatterns observed inclimatology [10], the latterpoint enables stochasticapproaches to be taken, whichare developed in the followingslide, with use of hybridMOGA technique.

The characters shown in TableII display a Pareto distributionwhen distributed over thecombined objective (wind andsolar) Z plane. Thedistribution is orthogonal tothat of the plant systemsblock, as shown in Figure 6(combined objectives 1 and 2are water and energy) forplant systems and Figure 7(combined objectives 3 and 4are wind and solar) forrenewable energy systems.


MOGA dispersal of Plant system and Renewable Energy system blocks

Evolutionary Strength Paretos of Blocks showing dispersal of characteristics


Fig. 6. MOGA Evolutionary Strength Pareto Front for Plant

Systems of E7.

Fig. 7. Orthogonal distribution of Renewable Energy Systems.

In Figure 6, Linear Utopia Rule is given by: (3) Where is -0.11, is -0.16 and is 0.58246.

Quadratic Utopia Rule is given by: (4) Where is 0.0014, is 0.0014, is0.0078 and is 0.033382.Cubic Utopia Rule is given by: (5) Where is -0.00034, is 0.0091, is 0.0018, is 0.00045 and is 0.0023036.

1 2

1 2

1 2 34

3

Domain flipping functions, Lyapunov stability showing convergence of coupled system blocks

Figure 6 (combined objectives 1 and 2 are water and energy) for plant systems and Figure 7 (combined objectives 3 and 4 are wind and solar) for renewable energy systems.

Equations (3), (4) and (5) are summarized within the generic framework of a Pareto distribution is given by:

(6)

Where F represents the function of the data i in the space of Figure 6, M represents the midpoint of the utopia front (indicated on Figure 6) and B represents the Z matrix space. To see the opposite/orthogonal population we simply change the upper bound of each function to its lower bound as follows:

(7)

The points of convergence between the two system blocks are reached at the start and end points of the MOGA evolutionary strength population (min x, max y; max x, min y) within the limits of 1, 2, 3, n, with exponentially decreasing error. The min and max of each objective plane represent the climatic data shown in Figures 1-4.

At convergence points the systems show Lyapunov stability as they have the following characteristic:

(8)

Where is ‘for all’, is ‘there exists’, represents the differential, x represents the data shown of plant systems, y represents data of renewable systems, is ‘element of’, X is the generic plant system data function, including other types than that shown here, n is set value number, N is generic number, d is ‘difference’, is ‘approaches’, fn

is function.


Application of fuzzy sliding mode to illustrate convergence between coupled system blocks.

As the populations of each block increases in its dispersal away from the max x, min y; min x, max y, the systems become Lyapunov asymptotic:

(9)

In alternative terms, more conducive to ‘feed forward’ or ‘feeding back’ within the two systems fuzzy sliding mode may be used by stating further candidate Lyapunov functions:

(10)

Where the vector x is equal to the function of x multiplied by inputs (u) into the system.

Different sliding mode controllers must be designed for each orthogonal system and convergence and values of each population identified via use of combinatorial genetic algorithm-Lyapunov functions.


Conclusions and Discussion – System Alignments and their value


Uncertainty within plant systems and renewable systems was quantified using T-S-K fuzzy logic.

This study has made use of hybrid MOGA-Fuzzy Techniques to create system blocks representing plantgrowth systems / renewable energy systems. Elements of each system were dispersed within dynamicswhich share similar functions.

Chromosomes of plant systems were distributed in the water-energy dynamic variables of precipitationand temperature.

Chromosomes of renewable systems were distributed in IPCC projected easterly wind and shortwave flux.

ANFIS nodal diagrams represent the efficiency of algorithms. Further linear, quadratic and cubic rules werederived with exponential decreasing error and hence increased rational pattern distribution [11].

Each Pareto dispersed block was shown using combined objective axis in 2 of the 4 dimensions-precipitation, temperature, easterly wind and shortwave flux. Convergence between the system blocks wasshown by ‘domain flipping’ [12].

Sliding mode was used in the design problem of aligning renewable energy development with that ofproductive plant systems. The orthogonal blocks of plant and renewable systems display Lyapunov stability,further investigation of hybrid Sliding Mode systems [13], [14] are suggested in the design of controllers forthe respective systems which will lead to the development of sustainable plant systems powered usingrenewable sources of energy, with great market value and socio-economic benefit.

References[1] J. Furze, Q. Zhu, F. Qiao and J. Hill, “Functional enrichment of utopian distribution of plant life forms,” American Journal of Plant

Sciences, Vol. 4, No. 12A, 2013, pp. 37-48.

[2] J. Furze, Q. Zhu, F. Qiao and J. Hill, “Implementing stochastic distribution within the utopia plane of primary producers using ahybrid genetic algorithm,” International Journal of Computer Applications in Technology, Vol. 41, No. 1, 2013, pp. 68-77.

[3] M. New, M. Hulme, and P. Jones, “Representing twentieth century space-time climate variability. Part I- Development of a 1961-90 mean monthly terrestrial climatology,” J. Climate, Vol. 12, 1999, pp. 829-856.

[4] J. Furze, J. Hill, Q. M. Zhu, F. Qiao, "Algorithms for the Characterisation of Plant Strategy Patterns on a Global Scale," AmericanJournal of Geographic Information System, Vol. 1, No. 3, 2012, pp. 72-99.

[5] Core Writing Team, R. K. Pachauri and A. Reisinger, (Eds.), Contribution of Working Groups I, II and III to the Fourth AssessmentReport of the Intergovernmental Panel on Climate Change, IPCC, Geneva, Switzerland, 2007.

[6] M. Z Jacobsen and C. L. Archer, “Saturation wind power potential and its implications for wind energy,” PNAS, Vol. 109, No. 39,2012, pp. 15679-15684.

[7] M. Mazandarani and M. Najariyan, “Differentiability of type-2 fuzzy number–valued functions,” Commun. Nonlinear SciNumerSimulat., Vol. 19, 2014, pp. 710-725.

[8] F. Qiao, Q. Zhu and F. Zhang, (2008) “Adaptive observer based nonlinear stochastic system control with sliding modeschemes,” Proceedings of the Institution of Mechanical Engineers, Vol. 222, 2008, pp. 681-690.

[9] A. Fouad, D. Boukhetela and F. Boudjema, “Decentralized sliding mode controller based on genetic algorithm and a hybridapproach for interconnected uncertain nonlinear systems,” International Journal of Control & Automation, Vol. 6, 2013, pp. 61-86.

[10] B. F. Farrel and P. J. Ioannou, “Structure and spacing of jets in barotropic turbulence,” Journal of Atmospheric Sciences, Vol. 64,2006, pp. 3652-3665.

[11] Q. Zhu, Y. Wang, D. Zhao, S. Li and S. A. Billings, “Review of rational (total) nonlinear dynamic system modelling, identificationand control,” International Journal of Systems Science, 2013, pp. 1-12.

[12] S. V. Utyuzhnikov, and D. V. Rudenko, “An adaptive moving mesh method with application to non-stationary hypersonic flows inthe atmosphere,” Proc. IMechE,, Vol. 222, 2007, pp. 661-671.

[13] X. Wei and L. Guo, “Composite disturbance-observer-based control and terminal sliding mode control for non-linear systemswith disturbances,” International Journal of Control, Vol. 82, 2009, pp.1802-1098.

[14] F. Qiao, Q. Zhu and B. Zhang, Fuzzy sliding mode control and observation of complex dynamic systems and applications, BeijingInstitute of Technology Press, China 2014.


Author Contact details for any questions

• Dr. James Furze (Corresponding Author)

Email: [email protected]

• Prof. Quanmin Zhu

Email: [email protected]

Thank you for your attention!
