Stabilizing control for a class of delay unstable processes

A simple derivation of all stabilizing proportional controllers for first order time‐delay systems

“…In [10], the entire set of PI and PID controllers for first order time-delay integrator processes is calculated combining the D-partition and the graphical techniques. This work is extended to different types of unstable processes in [19][20][21]. This method is based on the calculation of admissible values of k p for which a stabilizing set of k i and k d can be found.…”

Stabilisation of unstable FOPDT processes with a single zero by fractional-order controllers

“…Equation (9) is the normalised transfer function obtained from the following more general transfer function as described in (Lee et al 2010b).…”

“…NðsÞ and DðsÞ are functions of s, which satisfy Nð0Þ ¼ 1 and Dð0Þ ¼ 1.The stabilisability problem of the open-loop transfer function (14) has been dealt with in Lee et al (2010b), while v is a nonnegative integer number which represents the type of the system. In this article, v can be an integer or a non-integer number belonging to the range [0,2).…”

All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

“…By employing the well-known Nyquist stability criterion, many graphical-based stabilizing controller results are available for time delay systems with different limitations [6][7][8][9][10][11]. As well as the graphical-based results, there are also many studies about the analytical characterization of all-stabilizing low-order controllers for time delay systems with different limitations [12][13][14][15][16][17][18].…”

“…In [12], all-stabilizing P-and PI-type controllers are computed for this type of system, but they consider the open-loop unstable plants only. Additionally, the algorithm proposed in [28] can be considered a general method to compute all-stabilizing P controllers, which may be utilized for transfer functions of many kinds.…”