Positive real control for descriptor systems with uncertainties in the derivative matrix via a proportional plus derivative feedback

Pole Placement for Single-Input Linear System by Proportional-Derivative State Feedback

“…The PD controller is the most widely used controller structure in a wide range of practical applications (see Refs. [16][17][18][19][20][21][22][23] and the references therein). Its structural simplicity and sufficient ability of solving several practical control problems have contributed to this wide acceptance.…”

“…Many kinds of controllers have been proposed, such as proportionalintegral-derivative (PID) [13][14][15], PD [13,[16][17][18][19][20][21][22][23], PI [24,25], and state-derivative (D) [11,12,[26][27][28][29][30]. Recently, several researchers have been extended the concept of pole placement for LTI singleinput models to utilize PID state feedback [13,14], PD state feedback [13] and fractional PI state feedback [25].…”

“…[19]. For descriptor systems, the PD state feedback control has been intensively and widely studied [20,21]. For these systems, the PD feedback is an even more significant type of feedback, in which the additional state-derivative term can be used to eliminate the impulse behavior as well as to change the dynamical order.…”

Robust pole assignment using velocity–acceleration feedback for second-order dynamical systems with singular mass matrix

“…The researchers have recognized the importance of using derivative feedback on diverse practical engineering fields, such as vibration suppression in mechanical systems and flexible structures where the accelerometer is the only sensor. Moreover, the problem of statederivative feedback has been investigated within the treatment of a generalized class of first-order singular linear systems [15]. Consequently, the derivative feedback control has been applied to design numerous kinds of practical systems.…”

“…Recently, some new results on the eigenstructure assignment for the second-order system with a singular mass matrix are developed in [12]. The first-order descriptor systems (singular systems or generalized systems) have been of great interest in the specialized literature because they have many practical applications in robotics, mechanical systems, electrical circuit networks, economics and other areas; see [13][14][15] and the references therein. Up to date, no results on robust pole assignment control problem for descriptor second-order linear systems are available in the literature using combined acceleration and velocity feedback, this problem is still open.…”