Vector envisionment (VE) is a qualitative modelling method, for reasoning about dynamic physical systems, based on qualitative vectors. A qualitative vector is a means of describing the shape of a continuously differentiable, monotonic, real valued, function of time. It consists of a list of elements representing the qualitative value of the function along with the qualitative value of its successive derivatives; and an envisionment is the set of all possible qualitative behaviours that a system may exhibit for a particular input. This can be contrasted with a simulation which should produce a unique behaviour. Compartmental systems are a class of dynamic system composed of a finite set of homogeneous, well mixed, lumped subsystems called compartments; the behaviour of each compartment may be described by a first order differential equation. A linear time invariant one compartment system is analysed for all increasing monotonic input vectors and it is demonstrated that VE can find all the distinct qualitative states in which the system may exist for a given input. The analysis is performed by associating a polynomial of appropriate length with each vector and using this to interpret the results of the envisionment. From this analysis a solution space is constructed which is divided in accordance with the critical points of the system. Each qualitatively distinct region of this space is associated with a particular range of magnitudes for the initial values for the state variable. An examination of the results gives a means of overcoming the problem of chattering. VE is applied to examples of cascaded and coupled two compartment systems for a step input. Analysis shows that all and only the valid states of the system are again produced.
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