The paper proposes a procedure for design of PI controllers for hydraulic systems with long transmission lines which are described by models of high order. Design is based on the combination of the IE criterion and engineering specifications (settling time and relative stability) as well as on the application ofD-decomposition. In comparison with some known results, the method is of graphical character, and it is very simple (solving nonlinear algebraic equations is eliminated). The paper presents the algorithm of software procedure for design of the controller. The method is compared with other methods at the level of simulation, and its superiority is shown. By applying the Nyquist criterion, it is shown that the method possesses robustness in relation to non modelled dynamics.
The paper presents the problems of describing the system of a pump-controlled motor with a long transmission line by means of a mathematical model with lumped parameters where the long transmission line is divided into n segments. The mathematical model thus obtained is of high order but its order is reduced by applying the appropriate methodology, which considerably increases its use value. A P controller was designed for that mathematical model of the system. The graphical method which includes performances (specification of damping of the system) and stability margins was used in the design. Thanks to strong software support, the complexity of synthesis of controllers was considerably reduced in comparison with the methods presented in the literature. Dynamic behavior of the closed loop system was treated in intensive simulation. The methodology applied provides significant energy savings. penbetriebenen Motors mit einer langen hydraulischen Leitung vorgestellt. Das entwickelte mathematische Modell hö-herer Ordnung wird derart vereinfacht, dass seine Handhabung deutlich vereinfacht wird. Für dieses System wird ein P-Regler verwendet. Für den Entwurf wird eine graphische Methode benutzt, die die Kennlinien unter Angabe der Dämpfung des Systems und die Randstabilität einbezieht. Dank der Softwareunterstützung wurde die Komplexizität der Reglersynthese, im Vergleich zu bekannten Methoden der Literatur, bedeutend reduziert. Mit einer intensiven Modellierung wurde das dynamische Verhalten des Systems in einer geschlossenen Kopplung betrachtet. Die Methodologie, die angewendet wurde, ermöglicht bedeutende Energieersparnisse.
List of symbolsA (m 2 ) cross section area A L , B L , C L , D L coefficients of the transfer matrix a i , a k , b k coefficients of the transfer function B (N m −2 ) module of compressibility B v (N m s) friction viscosity C (m 4 N −1 ) capacity of the transmission line C 1 (m 5 N −1 ) capacity of the transmission line C m , C p (m 5 N −1 ) capacity of the motor and the pump c (m s −1 ) speed of sound in the fluid D m , D p (m 3 rad −1 ) motor and pump displacement d (m) diameter of the transmission line E (N m −2 ) equivalent module of elasticity (fluid-pipe) g m gain margin J m (kg m 2 ) motor load inertia K a (m 3 V −1 rad −1 ) coefficient voltage-pump displacement K p gain P controllers K T G (V s rad −1 ) coefficient of the tacho-generator 232 Forsch Ingenieurwes (2011) 75:231-242 L (kg m −5 ) inductivity of the transmission line L 1 (kg m −4 ) inductivity of the transmission line l (m) length of the transmission line n number of segments of the long transmission line n p (rps −1 ) number of revolutions of the pump p 1 , p 2 , p n (Pa) pressure Q 1 , Q 2 , Q n (m 3 s −1 ) flow R (N s m −6 ) resistance of the transmission line R 1 (N s m −5 ) resistance of the transmission line R m , R p (N s m −5 ) resistance leakage of the motor and the pump s complex number s m stability margin T L (N m) external load T (ξ), U(ξ) Chebyshev functions of the first and second kinds t (s) time V (m 3 ) volum...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.