Inversion-based feedforward control design for linear transport systems with spatially acting input

ABSTRACT

The considered transport systems, which possess an actuator with a spatial influence characteristic along the transport path, are used for the transport of material between different process stages and for the conditioning of the conveyed goods at the same time. The spatially acting input results in complex input/output behaviour of a Single-Input Single-Output (SISO) system with distributed delays. The feedforward control task under consideration is defined by a setpoint change of the subsequent process stage. For the feedforward controller design, an inversion-based approach in the frequency domain is investigated to steer the output of the transport system towards a predefined constant value. In order to compensate model uncertainties and reject unknown disturbances, the results of the inversion-based feedforward control are used to design a feedback controller.

KEYWORDS:

• Linear transport system
• distributed delays
• inversion-based feedforward control
• frequency domain design
• two-degrees-of-freedom control structure

Acknowledgment

The authors gratefully acknowledge the constructive comments of the reviewers.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The expansion (4.2) of the inverse transfer function (14(14) $$\begin{array}{cc}\hfill F\left(s\right)& =\underset{F_1\left(s\right)}{\underbrace{\frac{P_1\left(s\right)}{\Delta \left(s\right)}}}{e}^{-T_{1}s}+\underset{F_2\left(s\right)}{\underbrace{\frac{P_2\left(s\right)}{\Delta \left(s\right)}}}{e}^{-T_{2}s}\text{with}\hfill \\ \hfill P_i\left(s\right)& ={(-1)}^i{e}^{-\alpha T_i}\sum _{k=1}^{\nu }\sum _{j=0}^{p_k-1}{(-v)}^j{\Delta }_k\left(s\right){\omega }_k^{p_k-(j+1)}\left(s\right){\rho }_k^{\left(j\right)}\left(z_i\right)e^{{\lambda }_k{z}_i},\hfill \\ & i=1,2,\hfill \\ \hfill {\omega }_k\left(s\right)& =s+\alpha +{\lambda }_{k}v,\Delta \left(s\right)=\prod _{l=1}^{\nu }{\omega }_l^{p_l}\left(s\right),{\Delta }_k\left(s\right)=\prod _{\begin{array}{c}l=1\\ l\ne k\end{array}}^{\nu }{\omega }_l^{p_l}\left(s\right),\hfill \\ & n=\sum _{k=1}^{\nu }{p}_k.\hfill \end{array}$$(14) ) by the non-entire function $F_2^{-1}\left(s\right)e^{T_{2}s}$ is a design step for the inversion-based feedforward control and may lead to a loss of controllability. However, it does not affect the feedforward control design based on the inverse I/O model (14).

Additional information

Funding

This work was supported by Deutsche Forschungsgemeinschaft [grant number SA-847/6-2].