Abstract
The paper deals with tuning the filtered PID controller applied to third order plants with delay. This model option is chosen as a representative case where the loop characteristic quasi-polynomial is of higher order than three. Applying the similarity theory for introducing dimensionless parameterization a comparative model of third order plant dynamics is obtained. Four dominant poles – from the infinite spectrum of the control loop – are assigned by means of tuning three controller gains and a filter time constant where a specific argument increment criterion proves their dominance. The pole prescription coordinates are parameterized via damping, root and natural frequency ratios optimized in the space of the introduced similarity numbers according to the IAE criterion with respect to robustness and filtering constraints. Particularly the natural frequency ratio is a new parameter introduced to tune robustly the PID together with its filter. For the constrained IAE optimization the response of disturbance rejection is used as a representative of control loop behavior. In the space of similarity numbers of the plant it is shown that a limited range of plants is suited to be controlled on the PID control principle and the boundaries of this range are outlined. Survey maps of optimum controller parameters are presented and a comparative study on benchmark application example is added.
Highlights
In industry the most frequent output driven control is provided by a PID-type structure controller, even for systems with significant time delay [1]
These tunings are based on ultimate cycle identification, various performance index minimizations, gain, phase and jitter margin specifications, magnitude optimum method, pole placement technique or IMC-like tuning, which are well suited for non-dominant delay processes, except for the IMC-like tuning, [8], and the dominant pole placement, [9]
The former tuning is suitable for dominant delay processes assuming safe pole-zero cancellation in the open loop [10], in [11] this cancellation is modified to systems with large time delay and in [12] the IMC-like PID with a second-order lead-lag filter compensates for the dominant plant poles and zeros
Summary
In industry the most frequent output driven control is provided by a PID-type structure controller, even for systems with significant time delay [1]. There are many PI(D) tuning rules for the first- or second-order plants with a delay which is regularly approximated by the Padé or Taylor series [2]-[7] These tunings are based on ultimate cycle identification, various performance index minimizations, gain, phase and jitter margin specifications, magnitude optimum method, pole placement technique or IMC-like tuning (so-called Lambda tuning), which are well suited for non-dominant delay processes, except for the IMC-like tuning, [8], and the dominant pole placement, [9]. The novelty of the dominant pole placement approach consisting in the frequency ratio prescription brings robust PID and filter settings for the sets of dynamically similar third-order plants with delay. The optimum controller and filter parameters are mapped to show varying delay effect
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