Feedforward for Robust Reference Tracking in Multi-Input Feedback Control

Abstract

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.

Feedforward of Measurable Disturbances to Improve Multi-Input Feedback Control

“…An appropriate control must compensate for the output deviation from the constant reference, e = r − y, when a d disturbance occurs; reference tracking problems were discussed in [13]. Measurable disturbances are considered in the new design method.…”

“…The goal is to find the solution that uses the set of smaller control inputs u i /d. The authors of [13] provided a method for the problem of robust reference tracking (r = constant). The key point was the more the gain of a plant, the less the need of control action to contribute to the performance, which foresaw the use of inputs towards plants with higher gains at each frequency.…”

“…The availability of multiple inputs made it possible to select the intervention of the more favourable plants p i at each frequency to achieve |e/d| < W d using the minimum |u i /d|. Individual feedforward g d i and individual feedback c i either disconnected or not the commanded inputs at each frequency; integrators or derivators are recommended to connect or disconnect plants at low frequency to fully eliminate steady-state errors [13]. Further, c i and g d m were in charge of providing |e/d| < W d ; let us recall that g d i were filters of unitary gain at the pass-band.…”

“…Some works focused on widening the range of operating points for the output [5,6]. Other works focused on improving the output dynamic performance and simultaneously searched for a profitable combination of control inputs, branding them as input (valve) position control, mid-ranging control [7], or input resetting control [8]-their foundation [9] has inspired a set of works in the robust framework of QFT with the named missions of feedback and feedforward [10][11][12][13]. Thus, the robustly designed control elements determine the intervention or inhibition of plants (one for each input) along the frequency band.…”

“…The reference tracking problem admits feedforward elements that can reduce the gain of feedback controllers to palliate noise amplification at control inputs [13]. Beyond that, the priority of the method in [13] was achieving correct distribution of the bandwidth among the inputs (plants) to obtain the performance using the minimum possible control action at each input.…”