Abstract
The context of this paper is the application of electrical circuit synthesis to problems of mechanical control. The use of the electrical-mechanical analogy and the inerter mechanical element is briefly reviewed. Classical results from passive network synthesis are surveyed including Brune’s synthesis, Bott-Duffin’s procedure, Darlington’s synthesis, minimum reactance extraction and the synthesis of biquadratic functions. New results are presented on the synthesis of biquadratic functions which are realisable using two reactive elements and no transformers.
This research was partially supported by the Office of Naval Research under Grant N00014-02-1-0011, N00014-05-1-0186, and by the National Science Foundation under Grants ECS-0122412 and INT-0128656. The first author also acknowledges the support of the Faculty Startup Grant at the University of Maryland.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anderson, B.D.O., Vongpanitlerd, S.: Network Analysis and Synthesis: A Modern Systems Theory Approach. Prentice Hall, Englewood Cliffs (1973)
Auth, L.V.: Synthesis of a Subclass of Biquadratic Immittance Functions, PhD thesis, University of Illinois, Urbana, 111. (1962)
Auth, L.V.: RLC Biquadratic Driving-Point Synthesis using the Resistive Threeport. IEEE Trans. on Circuit Theory, 82–88 (1964)
Baher, H.: Synthesis of Electrical Networks. Wiley, Chichester (1984)
Balabanian, N.: Network Synthesis. Prentice-Hall, Englewood Cliffs (1958)
Belevitch, V.: Summary of the history of circuit theory. Proc. IRE 50(5), 848–855 (1962)
Bott, R., Duffin, R.J.: Impedance synthesis without use of transformers. J. Appl. Phys. 20, 816 (1949)
Brune, O.: Synthesis of a Finite Two-terminal Network Whose Driving-Point Impedance is a Prescribed Function of Frequency. J. Math. Phys. 10, 191–236 (1931)
Cauer, W.: Die Verwirklichung von Wechselstrom-Widerstanden Vorgescriebener Frequenzabhängigkeit. Arch. Elektrotech. 17, 355 (1926)
Cauer, W.: Synthesis of Linear Communication Networks. McGraw-Hill, New York(1958)
Cederbaum, I.: Conditions for the impedance and admittance matrices of n-ports without ideal transformers. Proc. IEE 105, 245–251 (1958)
Cederbaum, I.: Topological considerations in the realization of resistive n-port networks. IRE Trans, on Circuit Theory CT-8(3), 324–329 (1961)
Chen, M.Z.Q., Smith, M.C.: Mechanical networks comprising one damper and one inerter, Technical Report, CUED/F-INFENG/TR.569, Cambridge University Engineering Department, England (December 2006)
Chen, M.Z.Q., Smith, M.C.: Mechanical networks comprising one damper and one inerter. In: Proceedings of European Control Conference, Kos, Greece, pp. 4917–4924 (2007)
Chen, M.Z.Q.: Passive Network Synthesis of Restricted Complexity, PhD thesis, University of Cambridge, Cambridge, UK (2007)
Darlington, S.: Synthesis of reactance 4-poles which produce prescribed insertion loss characteristics. J. Math. Phys. 18, 257–353 (1939)
Darlington, S.: A History of Network Synthesis and Filter Theory for Circuits Composed of Resistors, Inductors, and Capacitors. IEEE Trans, on Circuits and Systems 46(1) (1999)
Dewilde, P., Viera, A.C., Kailath, T.: On a Generalized Szegö-Levinson Realization Algorithm for Optimal Linear Predictors based on a Network Synthesis Approach. IEEE Trans, on Circuits and Systems 25, 663–675 (1978)
Evangelou, S., Limebeer, D.J.N., Sharp, R.S., Smith, M.C.: Control of motorcycle steering instabilities—passive mechanical compensators incorporating inerters. IEEE Control Systems Magazine, 78–88 (October 2006)
Evangelou, S., Limebeer, D.J.N., Sharp, R.S., Smith, M.C.: Mechanical steering compensation for high-performance motorcycles. Transactions of ASME, J. of Applied Mechanics 74(2), 332–346 (2007)
Fialkow, A., Gerst, L: Impedance synthesis without mutual coupling. Quart. Appl. Math. 12, 420–422 (1955)
Foster, R.M.: A reactance theorem. Bell System Tech. J. 3, 259–267 (1924)
Foster, R.M., Ladenheim, E.L.: A Class of Biquadratic Impedances. IEEE Trans. on Circuit Theory 10(2), 262–265 (1963)
Foster, R.M.: Biquadratic impedances realizable by a generalization of the five-element minimum-resistance bridges. IEEE Trans, on Circuit Theory, 363–367 (1963)
Foster, R.M.: Comment on Minimum Biquadratic Impedances. IEEE Trans. on Circuit Theory, 527 (1963)
Garnett, J.B.: Bounded Analytic Functions. Academic Press, London (1981)
Guillemin, E.A.: Synthesis of Passive Networks. John Wiley, Chichester (1957)
Newcomb, R.W.: Linear Multiport Synthesis. McGraw-Hill, New York (1966)
Pantell, R.H.: A new method of driving point impedance synthesis. Proc. IRE 42, 861 (1954)
Papageorgiou, C., Smith, M.C.: Positive real synthesis using matrix inequalities for mechanical networks: application to vehicle suspension. IEEE Trans. on Contr. Syst. Tech. 14, 423–435 (2006)
Reza, F.M.: A Bridge Equivalent for a Brune Cycle Terminated in a Resistor. Proc. IRE 42(8), 1321 (1954)
Reza, F.M.: A supplement to the Brune synthesis. AIEE Communication and Electronics 17, 85–90 (1955)
Richards, P.I.: A special class of functions with positive real parts in a half-plane. Duke J. of Math. 14, 777–786 (1947)
Seshu, S.: Minimal Realizations of the Biquadratic Minimum Functions. IRE Trans. on Circuit Theory, 345–350 (1959)
Slepian, P., Weinberg, L.: Synthesis applications of paramount and dominant matrices. In: Proc. Nat. Elec. Conf., vol. 14, pp. 611–630 (1958)
Smith, M.C., Walker, G.W.: A mechanical network approach to performance capabilities of passive suspensions. In: Proceedings of the Workshop on Modelling and Control of Mechanical Systems, pp. 103–117. Imperial College Press, Imperial College, London (1997)
Smith, M.C.: Force-controlling mechanical device, patent pending, Intl. App. No. PCT/GB02/03056 (July 4, 2001)
Smith, M.C.: Synthesis of mechanical networks: the inerter. IEEE Trans. Automatic Control 47(10), 1648–1662 (2002)
Smith, M.C., Wang, F-C: Performance benefits in passive vehicle suspensions employing inerters. Vehicle System Dynamics 42, 235–257 (2004)
Storer, J.E.: Relationship between the Bott-Duffin and Pantell Impedance Synthesis. Proc. IRE 42(9), 1451 (1954)
Tellegen, B.D.H.: Théorie der Wisseistromen, P. Noordhoff (1952)
Tow, J.: Comments on On Biquadratic Impedances with two reactive elements. IEEE Trans. on Circuits and Systems 19 (1972)
Van Valkenburg, M.E.: Introduction to Modern Network Synthesis. Wiley, Chichester (1960)
Vasiliu, C.G.: Series-Parallel six-element synthesis of the biquadratic impedances. IEEE Trans. on Circuit Theory, 115–121 (1970)
Vasiliu, C.G.: Four-reactive six-element biquadratic structure. IEEE Trans. on Circuit Theory (1972)
Weinberg, L.: Report on Circuit Theory, Technical Report, XIII URSI Assembly, London, England (September 1960)
Yengst, W.C.: Procedures of Modern Network Synthesis. MacMillan, NYC (1964)
Youla, D.C., Tissi, P.: TV-port synthesis via reactance extraction, part I. IEEE International Convention Record, 183–205 (1966)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, M.Z.Q., Smith, M.C. (2008). Electrical and Mechanical Passive Network Synthesis. In: Blondel, V.D., Boyd, S.P., Kimura, H. (eds) Recent Advances in Learning and Control. Lecture Notes in Control and Information Sciences, vol 371. Springer, London. https://doi.org/10.1007/978-1-84800-155-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-84800-155-8_3
Publisher Name: Springer, London
Print ISBN: 978-1-84800-154-1
Online ISBN: 978-1-84800-155-8
eBook Packages: EngineeringEngineering (R0)