Transient Response Characteristics

Abstract

By using a computer program of the type described in the previous two chapters, we are in a position to analyse complex systems in both the frequency and time domains. Nevertheless it is instructive to examine some basic trends, particularly in the time domain, to enhance our system design capability. As an example we shall extend the treatment of the simple third order system, represented by the transfer functions eqns (11.16), (11.19) and (11.20), into the time domain. By means of the optimization algorithms described in Chapter 13, we can establish the equivalent system parameters corresponding to the limiting loop gain, plotted in Fig. 11.5 as a function of the hydraulic transmission damping factor, ζ. It can be seen from the graph of Fig. 15.1 that the natural frequency of the equivalent system ω_n is 67% of the hydraulic transmission natural frequency ω₀ up to a value of 0·6 hydraulic transmission damping factor ζ. At larger values of ζ, the system to hydraulic transmission natural frequency ratio diminishes. The system damping factor ζ_n reaches a minimum value of 0·34 at the optimum loop gain operating condition of ζ = 0·6. It is of interest to note that up to the optimum loop gain operating condition, low hydraulic transmission damping results in high system damping, whereas beyond the optimum condition system damping remains virtually constant.