Robust absolute stability analysis of a temperature control system for an enclosed space

Research methods of a heated space temperature adjustment system with respect to endogenous and exogenous uncertainties

“…Q -thermal energy coming from a heater; The analysis of the transfer function ‫)(ܹ‬ and the time constant T b of the heated space indicates that the system under consideration contains the following uncertainties [6,7]: a) exogenous (depends on exterior temperature); b) endogenous (depends on the supplied thermal energy and the heated space mass). The problem to be set is to study the heating system as a discrete one taking into account influence of temperature and other uncertainties on robust stability.…”

“…At present, a great number of published papers are devoted to the study of robust stability of control systems. These studies are carried on by means of both analytical [14,15] and graphical analytic methods [17,18].…”

“…When using the analog of Y.Z. Tsipkin criterion after the w-transformation and transition to the pseudofrequency jν, we get the following criterion which will be written in the form [17] ܴ݁ ቂቀ1 + ‫ݍ‬ Graphically the given criterion represents a modified amplitude-phase characteristic drawn in the plane ܹ * ෪ (݆ߥ). Just here, separated by a dot 1/k we draw a Popov straight line with a slope of 1/q.…”

“…Then we use the results of the strong theorem by V.L. Kharitonov [6]. As it follows from this theorem, a necessary and sufficient condition of the robust stability of the family of polynomials is to meet the Hurwitz criterion in the following four polynomials:…”

“…Besides, a digital control system makes it possible to control indoor temperature more precisely compared to analog/thermostat system where heating inertia can cause about 1.5 ° C indoor temperature variations resulting in thermal discomfort [3]. Modern systems of indoor temperature automatic control are the systems which function despite the availability of uncertainties of many types [4][5][6][7]. To take into account concomitant nonlinearities and other factors in mathematical models of temperature control systems which refer to nonlinear discrete automatic control systems (NDACS), it is necessary to apply special methods of research that could take into account not only structural peculiarities of NDACS, but also a model stability to uncertainties (robustness).…”