Tracking of a Thermodynamic Process using a Polytropic Surface as Sliding Manifold

The problem of driving the thermodynamic state of a substance towards a desired point, following a desired path, is considered here. The proposed method is shown for a simple system consisting of a fixed-volume chamber with input and output valves controlling the flow of substance, in this case an ideal gas. The model consists of a nonlinear, second-order system of differential equations with two inputs. Feedback linearization is used from one input to one of the controlled states, and the remaining state is controlled using sliding mode control, where the sliding manifold is precisely the thermodynamic path to be followed by the states as they progress towards the desired equilibrium. As an example, a polytropic process is chosen for the sliding regime. It is shown that the technique can achieve the objective even when an unmodelled but bounded heat transfer disturbance is present. Moreover, the availability of two degrees of freedom allows to independently specify the surface reaching time and the overall convergence time.