Abstract
We have proposed techniques using which made it possible to solve a nonlinear algebraic Riccati equation for dynamic systems with degrees of freedom. A constraint was imposed on the structure of a designed railroad carriage. We employed, as an analogue, a symmetrical carriage whose suspension system contains elastic-dissipative links with linear characteristics. This allowed us to devise a procedure for designing a suspension system for a railroad carriage. The criterion when choosing the weight coefficients of quality was the requirement to ensure comfortable conditions for passengers and a locomotive crew. Therefore, the system must experience an oscillatory process with small amplitudes; the frequency of natural oscillations of the body should not exceed 2 Hz. We have performed decomposition of the dynamic programming method for continuous stochastic systems, which made it possible to develop a procedure for a phased suspension system design. The procedure is suitable for use when designing suspensions for carriages running at regular and high-speed speed. The first stage implies designing a passive suspension system. The second stage involves a validation of the feasibility of designing devices to control parameters of the elastic-dissipative links in a suspension system of transport carriages using the optimal Kalman-Bucy filters. The modeling proved that control over parameters of elastic-dissipative links improves the dynamics of transport carriages. Damping control alone could reduce the body's center of mass acceleration by more than two times and hence decrease dynamic loads in the system. The Kalman-Bucy algorithm makes it possible to obtain optimal parameters of the elastic-dissipative links in a suspension system in complex dynamic systems. The procedure could be used independently and as part of the technique for a phased design of the suspension system. The procedure was demonstrated using test examples. The procedure is implemented in the simulation system. Control over parameters of the elastic-dissipative links in a suspension system of transport carriages would make it possible, first, to create comfortable working conditions for a locomotive crew and passengers, second, to improve operation reliability and motion safety of rolling stock by reducing dynamic loads.
Highlights
To obtain an accurate estimation of railway carriage run at the entire range of operating speeds, it is required to control suspension system parameters in terms of a possible change in the process of movement
When discusing control over a suspension system of transport carriages, it must be taken into consideration that as recently as in the mid-1980s many transport scientists did not believe in the possibility of constructing controlled suspension systems
The main task of analytical reviews of that period was to demonstrate the advantages of controlled vibration protection systems compared with traditional systems and to direct a scientific thought towards the development of various types of active suspension systems capable of providing the dynamic properties required for the carriage at a substantial increase in speed motion
Summary
To obtain an accurate estimation of railway carriage run at the entire range of operating speeds, it is required to control suspension system parameters in terms of a possible change in the process of movement. The theoretical studies carried out in these countries have shown that active suspension systems, which employ as a feedback signal acceleration or an absolute speed, make it possible to significantly improve running performance and motion stability of railroad carriages. Paper [8] reported a law of active control over a dual-mass mechanical system with two degrees of freedom using a method of dynamic programming for continuous stochastic systems. The authors could not resolve the issue on the choice of weights for the functional of quality though the reported results of mathematical modeling of the operation of an active suspension system shows its effectiveness; the amplitudes of displacements and body accelerations were reduced by two times. Creation of devices that would control parameters of the elastic-dissipative links in a suspension system is expensive and is justified when designing the rolling stock for high-speed motion. It is necessary to devise a procedure for verifying the feasibility of design of a controlled suspension system, in order to avoid unnecessary expenditures for the development of active control devices
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