Abstract
M.Ing.
Experimental tests have indicated that limit cycles are likely to occur in hydraulic drive systems, where backlash in the actuator seals is the dominant nonlinearity'. This study primarily deals with the analysis and synthesis of existing hydraulic drive systems to eliminate limit cycles and with establishing a design tool for the design of hydraulic drives with the object of avoiding limit cycles. Most analytical results were verified experimentally. The most general methods for the design of practical nonlinear systems
are discussed. It is concluded that some form of synthesis and analysis is necessary, and that the need exists for general methods to evaluate the stability of nonlinear systems and design tools for nonlinear system design. Ageneral procedure of system analysis is given. Amathematical model of the system needs to be obtained, which can be done with the aid of bond graphs. Simulations of complex systems are recommended to verify system performance only. The first procedure of system analysis that should be followed is to systematically identify elements of the system which are not related to the cause of the limit cycle. Experimental testing is a good first step in identifying the non-critical elements. Signal flow diagrams enable the engineer quickly to determine all feedback loops of a complicated system which might be critical. Block
diagrams are necessary for the application of nonlinear analysis and synthesis techniques. Hydraulic resonance, where the actuator seal acts as an oscillating
mechanism, is identified as a possible cause of the limit cycle. An unusual application of the describing function, where the describing function is applied to optimize the hydraulic supply, is discussed. The transfer function of flow in a hydraulic pipe is given. With the use of the describing function, the gain margin can be studied versus different
parameters of the plant. This gives insight into slightly damped conditions of the hydraulic supply that might be the cause of a limit cycle in the system. A control gain does not change the dynamic behaviour of the hydraulic supply, but only amplifies certain natural modes of the system. The design application of the describing function to nonlinear hydraulic drives is discussed. Procedures to eliminate an existing limit cycle and to design a nonlinear hydraulic drive system are proposed. Most important of all, is to design the system so that the natural frequencies of the mechanical structure and the hydraulic supply do not have any common multiples.