Stabilization of an inverted pendulum-cart system by fractional PI-state feedback

Robust Control of Positive Fractional‐Order Interconnected Systems with Heterogeneous Delays

“…Proof. By Theorem 1, the positive closed-loop system (4) is asymptotically stable if there exist vectors v i ∈ R n i , v i ≻ 0, satisfying condition (14). Consider the following transformation…”

“…Due to their widespread applications, for example, in mechanic, viscoelastic systems, dielectric polarization, electromagnetic waves, heat conduction or circuit systems, FO systems have been extensively studied in the past few decades [4][5][6][7]. Particularly, considerable research attention has been devoted to the problems of stability analysis [8][9][10] and controllers design including FO controllers synthesis for IO systems [11][12][13][14][15][16] and state/output feedback controllers synthesis for FO systems [17][18][19][20][21][22]. For example, based on a linear matrix inequalities (LMIs) approach, robust stability and stabilization problems were studied in [23] for FO linear systems with positive real uncertainties.…”

Stabilization of Single‐Input LTI Systems by Proportional‐Derivative Feedback

“…It is known that the state-feedback gain for a single-input system is in general unique for a given set of desired poles. Recently, several researchers have extended the pole assignment concept to utilize statederivative feedback [8][9][10][11][12], proportional-integral state feedback [13], and proportional-integral-derivative (PID) state feedback [14][15][16][17][18]. An approach of guaranteed dominant pole placement tuning for PID controllers to handle second-order systems was proposed in [16,17].…”

“…The feedback control principles are an appropriate tool in the analysis and design of linear control system strategies. Many kinds of controllers have been proposed, such as PID [14][15][16][17][18][19], proportional-derivative (PD) [20][21][22][23][24][25][26][27][28][29], and proportional-integral (PI) [13,30]. The control structures with PD state feedback sometimes are essential for achieving the desired control objectives, such as overshoot reduction in the responses, sensitivity reduction to parameter variations, and performance improvement of the control systems [31].…”

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

“…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]. The control structures with PD state feedback is sometimes essential for achieving the desired control objectives such as overshoot reduction in the responses, sensitivity reduction to parameter variations and performance improvement of the control systems [16,31].…”