ASHRAE Journal - August 2009 - 61

ASHRAE 19 50 59–2009 YE A R S JOURNAL Dynamic Criteria There are two criteria for system performance in the dynamic state. (1) transient response and (2) frequency response. Transient response refers to the response of a system to a single, or non-recurring, change of input, as for example, a step change. The output signal is recorded as a function of time. The equation of this timeoutput plot is used to determine a transfer function. This mathematical expression enables the engineer to predict and describe the complete system performance. Frequency response refers to the response of a system to a sinusoidally changing input. Again, the output is recorded as a function of time. From this plot, a ratio of output to input amplitude is made and the phase shift of output and input sinusoids is determined. These terms are then used to derive the transfer function of the system. In air-conditioning systems, response times are quite long and, as a result, frequency response techniques are seldom feasible on an actual system. F I G . 3 Transient response to a step change. F I G . 4 Response of an unstable system. Use of Transient Response Transient response data can be expressed by two indexes—overshoot and settling time. The proper combination of these determines the acceptability of the dynamic performance, just as offset determines the acceptability of the steady-state performance. Improvements in these indexes can be made by adjusting the controller gain or by using additional modes, such as rate action, and/or reset action. The purpose of system analysis is to enable the designer or operator to adjust the system so as to achieve the new steady state in as short a time as is consistent with the limitations of the equipment and in such a way as to maintain specified steady-state performance. STABILITY The fourth and last part of this paper deals with the most important characteristic of a control system—stability. Typical response curves as given in Fig. 2 were indicative of stable systems. Fig. 4, however, illustrates an unstable system. The significant difference in these two illustrations can be described in terms of the way the final value is reached after an input disturbance. Additionally, however, we have a system, as illustrated in Fig. 3, that for practical purposes can also be considered Au g u s t 2 0 0 9 a stable system and that reaches a final value in still a third manner. Let us consider these three classes of systems. They are overdamped, underdamped, and unstable. Overdamped systems, as illustrated in Fig. 2, gradually approach the final value, and at no time have an output signal that exceeds the desired final value. Underdamped systems, sometimes called oscillatory systems, are illustrated in Fig. 3. These systems oscillate about the final value several times, but with decreasing overshoot, until finally the amplitude of the oscillations falls within the offset band. Truly unstable systems, as illustrated in Fig. 4, oscillate about the final value indefinitely with increasing amplitudes until one or more of the components in the system saturates, at which time the amplitude of overshoot remains constant. ASHRAE Journal 61

ASHRAE Journal - August 2009

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