PID Control With Higher Order Derivative Degrees for IPDT Plant Models

Delay Equivalences in Tuning PID Control for the Double Integrator Plus Dead-Time

“…These are predominantly represented by peaks in the maximum sensitivity and complementary sensitivity functions (M s and M t ). Although the use of sensitivity functions is widespread, we are driven to replace them by several serious reasons: [27], but the required values may be much higher (see, for example, [29], who recommends M s ≈ 10, or [30], who works even with M s ≈ 20); (c) Potential counterproductivity: in terms of robust control design, the use of sensitivity functions can lead to counterproductive results [10].…”

“…In this concept, the non-integer derivative and integrative solutions are in the end approximated by HO filters. In contrast, in the concept of PID m n control [9,10] (generalized PID control with mth-order derivatives and nth-order low-pass filters), possibly including controllers with HO derivatives such as proportional-integral-derivative-accelerative (PIDA) control [11][12][13][14][15][16], the HO controllers are designed directly. As the main motivation for the FO-PID control, one can say that one tries to find more degrees of freedom.…”

“…As the main motivation for the FO-PID control, one can say that one tries to find more degrees of freedom. These should be used to specify the resulting control performance, robustness and measurement noise attenuation [8,10]. Mostly, application areas are mentioned in which the acquisition of a more detailed plant model is not possible or not reasonable.…”

“…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) models [10] and the conference paper [25], which compares the controller design for DIPDT systems using the performance portrait method with the multiple real dominant poles method.…”

“…A direct application of the MRDP method to control loops containing the filter dynamics in combination with the dead-time leads to complex formulas that are usually analytically incomprehensible. Therefore, similar to [10,20,46], simplified approaches based on replacing the filter transfer function by an equivalent dead time T e that can be simply added to the identified system delay T m (2) are used. This requires the use of the following approach:…”