Abstract
The paper proposes a feedforward boundary control to reject measured disturbances for systems modelled by hyperbolic partial differential equations obtained from conservation laws. The controller design is based on fre- quency domain methods. Perfect rejection of measured perturbations at one boundary is obtained by controlling the other boundary. This result is then extended to design robust open-loop controller when the model of the system is not perfectly known, e.g. in high frequencies. Frequency domain comparisons and time-domain simulations illustrates the good performance of the feedforward boundary controller.
Highlights
In this paper, we consider the control of plants whose models are hyperbolic partial differential equations obtained from conservation laws, with an independent time variable t ∈ [0, +∞) and an independent space variable on a finite interval x ∈ [0, L].The motivation of this work is related to the problem of controlling an openchannel around a given regime, represented by linearized Saint-Venant equations
We focus on the design of a feedforward control law in order to reject measured disturbances using boundary control
The rational approximations obtained with eq (12) are compared to KF (s) on figure 4
Summary
We consider the control of plants whose models are hyperbolic partial differential equations obtained from conservation laws, with an independent time variable t ∈ [0, +∞) and an independent space variable on a finite interval x ∈ [0, L]. In this case, we investigate how to design a rational compensator (the robust feedforward control problem). The above approaches have considered series decomposition of the feedforward controller, with a given order, leading to a given truncation error Another interesting possibility is to consider a finite bandwidth approximation of the feedforward controller, with a bounded error for higher frequencies. The previous approach has two possible drawbacks: (i) the plant model is assumed to be perfect, (ii) the irrational feedforward controller has to be approximated by a rational one.
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