Abstract
This paper presents a feedback control solution that achieves robust stability and disturbance rejection in systems with multiple manipulated inputs and a single measurable output. The uncertain plant models may exhibit either nonminimum phase, or delay, or unstable phenomena, which makes it not easy to take full advantage of the frequency response of each plant. In the framework of quantitative feedback theory (QFT), a methodology is proposed to decide the best control bandwidth distribution among inputs and to design the set of parallel controllers with as small as possible gain at each frequency. The temperature regulation in a continuous stirred-tank reactor (CSTR) illustrates the benefits of a quantitative frequency distribution of the dynamic controllability between the jacket flow and the feed flow. The main challenge is that the feed flow exhibits a higher temperature regulation capacity and also produces a temporary decrease in the reactor temperature (nonminimum phase behaviour).
Highlights
Nonminimum phase (NMP) behaviours are frequent in MISO process control. e design methods in [1, 2, 30] pay special attention to them inside serial arrangements of controllers. ose strategies make the inputs collaborate over different bands of frequency, such that the NMP input handles the low-frequency band and does not limit the achievable performance
Alvarez-Ramirez et al [9] illustrate how lessexpensive control effort can be obtained with the addition of redundant control inputs, but such a cost saving is obtained at the expense of a sluggish closed-loop response if any additional control input is of the NMP nature. us, the drawback of the method is that the inputs are forced to collaborate along the same frequency band
The slaves are designed bearing in mind the following issues: (a) they condition the zeros of the equivalent slaves-plants avoiding that they are located in the right half-plane (RHP) and may limit the achievable closed-loop performance; (b) they determine the relative magnitude contribution to the output; (c) the relative phase contribution may be critical if they are out of phase when their magnitude contribution is nearly the same
Summary
Placing the open-loop function exactly onto the bounds at each design frequency means using the minimum controller gain to achieve the specifications, which favours a smaller control gain beyond the gain cross-over frequency ωgc [32, 37], where feedback becomes useless or even harmful (e.g., high-frequency unmodeled dynamics or sensor noise amplification that can saturate the control input). Regardless of the bound height difference, a collaboration would always reduce the gain of controllers (let us remind the loops are not out of phase). These reductions may not justify the major complexity of performing the design. Over the frequencies where only one branch works, the MISO control is obviously equal to any SISO control (ω < 1)
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