Feedforward for Robust Reference Tracking in Multi-Input Feedback Control

This paper examines methods to incorporate feedforward loops of known external inputs (output reference) into a multi-input feedback control structure to achieve certain robust performance of its output. Undoubtedly, feedforward can reduce the need for feedback and therefore the amplification of sensor noise at actuators, as occurs in single-input control. Beyond that, since there are several available inputs, a convenient distribution of feedforward and feedback can minimise the control action at each input and offer benefits at all frequencies. The procedure is as follows: because there are rough plant models of the behaviour from each input to the output, it is possible to approximate the individual control demand that will satisfy the performance. Based on this, individual feedforward filters allocate the control bandwidth among the inputs in order to build an equivalent plant that has an equal or greater magnitude than any individual plant at each frequency. Next, the uncertainty of this equivalent plant is addressed by feedback that reduces the closed loop deviation of magnitude frequency responses. The reduction is sufficient to enable a master feedforward to place them, at a second step, around the desired tracking performance model without violating any deviation tolerances. Individual feedback controllers distribute the total feedback among the inputs in order to have the least possible feedback at each frequency. A first example illustrates the method and the relevance of a feedforward orientation to reduce the individual control action, instead of the individual feedback action. Another example proves the superiority of adding feedforward loops to feedback-only schemes and highlights the benefits of robust design methods such as Quantitative Feedback Theory (QFT). This paper also provides the algorithms to employ in response to new robust control specifications in the framework of QFT.