CHOICE OF SAMPLING INTERVAL
Whenever a digital control system is designed, a suitable sampling interval must be chosen. Choosing a large sampling time has destabilizing effects on the system. In addition, informa- tion loss occurs when large sampling times are selected. Also, the errors that occur when a continuous system is discretized increase as the sampling interval increases.
It may be thought that decreasing the sampling interval towards zero will make a discrete system converge towards an equivalent continuous system. However, in practice this is not the case since as the sampling interval is reduced, the change between the successive data values becomes less than the resolution of the system, leading to loss of information. In general, if a shorter sampling interval is to be used then the word length of the system should be increased so that the difference between adjacent samples can be resolved.
It has been found from practical applications in the process industry that a sampling interval of 1 s is generally short enough for most applications such as pressure control, temperature control and flow control. Systems with fast responses such as electromechanical systems (e.g. motors) require much shorter sampling intervals, usually of the order of milliseconds.
Various empirical rules have been suggested by many researchers for the selection of the sampling interval. These rules are based on practical experience and simulation results. Among them are the following
• If the plant has the dominant time constant Tp , then the sampling interval T for the closed- loop system should be selected such that T < Tp /10.
• Assuming that the process has a Ziegler–Nichols open-loop model
EXERCISES 267
• If the closed-loop system is required to have a settling time Tss or a natural frequency of ωn then choose the sampling interval T such that T < Tss /10 and ωs > 10ωn , where ωs is the sampling frequency, i.e. ωs = 2π/ T .