Non-linear sliding-mode controller and objective function for surge tanks

Abstract

A non-linear feedback controller is proposed for the ‘averaging’ control of surge tanks subject to step flowrate disturbances. The controller operates by discont-inuously switching between two non-linear feedback rules. A switching function is constructed that results in a sliding-mode that brings the system to a steady state with a finite, bounded, and ultimately monotonic response. The properties of the controller are thoroughly described using a phase plane analysis. The effects of transducer errors are analysed and a controller tuning procedure is described. It is shown that a liquid volume setpoint can be introduced if the relative volume measurement error is less than 26.42 %. A simplified implementation using a piece-wise linear switching function is also proposed for which simulations and phase plane analysis show little performance degradation. Finally, it is shown that (he idealized ‘Ramp Controller’ proposed by McDonald el al. (1986) can be derived from a continuous and differentiable objective function. The objective function is constructed for the maximum rate of change of outlet flowrate by formulating and solving an inverse optimal control problem.