Abstract
The paper investigates and explains a new simple analytical tuning of proportional-integrative-derivative (PID) controllers. In combination with nth order series binomial low-pass filters, they are to be applied to the double-integrator-plus-dead-time (DIPDT) plant models. With respect to the use of derivatives, it should be understood that the design of appropriate filters is not only an implementation problem. Rather, it is also critical for the resulting performance, robustness and noise attenuation. To simplify controller commissioning, integrated tuning procedures (ITPs) based on three different concepts of filter delay equivalences are presented. For simultaneous determination of controller + filter parameters, the design uses the multiple real dominant poles method. The excellent control loop performance in a noisy environment and the specific advantages and disadvantages of the resulting equivalences are discussed. The results show that none of them is globally optimal. Each of them is advantageous only for certain noise levels and the desired degree of their filtering.
Highlights
The range of methods suitable for controlling time-delayed systems is very large and growing
Before extending the design to controllers with HO derivatives and to controlled systems approximated by second-order time-delay models, it seems useful to show and analyze its essence and problems using the example of a PID controller with first-order derivatives
For the approximation of more complex real plant dynamics (models based on firstorder time-delayed systems are commonly used to control simpler systems [2]), the double integrator plus dead time (DIPDT) model
Summary
The range of methods suitable for controlling time-delayed systems is very large and growing (see, e.g., [1,2,3,4,5,6,7]). Application areas are mentioned in which the acquisition of a more detailed plant model is not possible or not reasonable These are areas that are extremely attractive because even small improvements in performance result in large economic gains: e.g., vehicle attitude control when driving on a road with a variable profile, control of highly nonlinear robotic systems and load frequency control of power plants. For the approximation of more complex real plant dynamics (models based on firstorder time-delayed systems are commonly used to control simpler (lower-order) systems [2]), the double integrator plus dead time (DIPDT) model. This paper develops further the results of the design of the HO-PID controller, which focus on the control of systems approximated by the integrator-plus-dead-time (IPDT).
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