A new methodology for designing PID controllers

It is known that it is impossible to select fixed gains for a PD controller that will critically damp the response to disturbances for all configurations of a given robot system. Because of this the potential for overshoot is always present and cannot be avoided unless the system is severely overdamped. This is not necessarily a practical solution and can be an economically unacceptable approach. On the other hand, however, if overshoot is permissible to some degree for some systems in the case of conventional Serial robots it is still prohibited in the case of Parallel robots as it may easily bring the robot to one of its possible singular configurations, causing damage to the system. This paper introduces a new algorithm for the design of PD controllers that ensures uniform and fast dynamic responses, which are free from overshoots for all robot configurations. The technique also satisfies general stability requirements for the system

Analiza stabilnosti nelinearnih sustava vođenih analitičkim neizrazitim regulatorom

Tema ove disertacije je analiza stabilnosti nelinearnih mehaničkih sustava vođenih analitičkim neizrazitim regulatorom. Analitički neizraziti regulator je nekonvencionalni pristup koji koristi analitičke funkcije za određivanje centara izlaznih neizrazitih skupova umjesto baze pravila ponašanja. Analiza stabilnosti je zasnovana na Lyapunovljevoj izravnoj metodi i ne zahtijeva prikaz dinamike sustava upravljanja u obliku Takagi- Sugeno neizrazitog modela. Analiza stabilnosti je podijeljena na četiri osnovna dijela. Prvo se formiraju jednadžbe pogreške zatvorenog sustava upravljanja. Drugo, formira se kandidat za Lyapunovljevu funkciju. Zatim se izvode uvjeti stabilnosti koji garantiraju pozitivnu definitnost Lypunovljeve funkcije i negativnu definitnost njene vremenske derivacije. Na kraju, primjenjuje se LaSalleov princip invarijantnosti koji garantira asimptotsku stabilnost. Time su dobiveni kriteriji lokalne stabilnosti koji uključuju svega nekoliko parametara upravljačkog sustava. Na osnovu dobivenih rezultata razmatrane su neke modifikacije analitičkog neizrazitog regulatora koje osiguravaju globalnu asimptotsku stabilnost. Nadalje, Lyapunovljeve funkcije analiziranih regulatora su iskorištene za evaluaciju performansi i određivanje optimalnih vrijednosti parametara regulatora. \Navedeni pristup zasnovan je na konstrukciji parametarski ovisne Lyapunovljeve funkcije. Odgovarajućim izborom slobodnog parametra dobivena je ocjena integralnog indeksa performanse. Indeks performanse ovisi samo o nekoliko parametara regulatora i nekoliko parametara koji karakteriziraju dinamiku robota. Optimalne vrijednosti parametara regulatora dobivene su minimizacijom indeksa performanse. Procedura podešavanja parametara demonstrirana je na simulacijskom modelu dva različita tipa robota

Dynamic analysis, design and control of an industrial parallel robot

An investigation into the applicability of the bond-graph methodology, using the so-called Model Transformation Tools software, has been undertaken to model parallel robots. This software is a novel, non-commercial, program developed at the University of Glasgow, and in addition to the standard bond graph, it contains a powerful tool called the Hierarchical Bond Graph for dealing with very large-scale dynamical systems. It is the first time this tool has been applied for the modelling of parallel manipulators. A General Method for modelling parallel robots using the Hierarchical Bond-Graph concept has been developed. The method is based on related work on the modelling of closed chain robots using the Lagrange method. Introduction of a new design concept to be known as the Multi-cell Parallel Planar Manipulator. The methodology allows for an increase in the workspace of the manipulator by increasing the number of cells without affecting the number of DOF. It can also be shown to enhance the manoeuvrability of the system. Application of the multi-cell approach to a specific 2-DOF planar parallel manipulator and recognition of the need for a general model led to the development of a general dynamic model for the multi-cell manipulator using the Lagrange method. The reason for using the Lagrange formulation is that the necessary generalisation cannot be formalised using the Bond Graph technique due to the dependency of a bond graph on the specified structure of the system being modelled. Static balancing of the new general manipulator was addressed and a new method for balancing has been introduced. The method reduces the number of parameters to be adjusted to only one