Tuning the leading roots of a second order DC servomotor with proportional retarded control

Tuning and noise attenuation of a second order system using Proportional Retarded control

“…Lemma 3. Villafuerte and Mondié (2010) Let k p ≥ 0 and σ ≥ 0 be given. The first stability region of the quasipolynomial (8) is defined as follows: Upper boundary: For the selected k p and σ , draw in the (h, k r ) plane…”

“…b-The three real dominant roots insure the best closed loop response in terms of oscillatory behavior attenuation. (see Villafuerte and Mondié (2010) for a detailed analysis) Some additional properties depicted in Figure 2 are the following:…”

“…Reference Villafuerte and Mondié (2010) presents a detailed frequency domain analysis of the σ -stability of the PR control law (1) in closed loop with system (2).…”

σ‐Stabilization of a Flexible Joint Robotic Arm via Delayed Controllers

“…In this framework, in [17], a method for the migration of a double imaginary characteristic root to the left half-plane or the right halfplane under the variation of two parameters of a quasipolynomial is presented. e idea of deliberately introducing time delays in closed-loop systems and considering it as a control parameter is not a novel approach, but it has been intensively studied in recent years, see [18][19][20] and the references therein. e analysis of such class of controllers focuses mainly on the following topics: characterization of the stability crossing curves [21], tuning of delayed controllers to stabilize second-order systems [18,20,22] (and its noise attenuation analysis [23]), the design of proportional integral controllers for second-order linear systems [19,24], and design of maximum decay rate using elimination theory [25].…”

“…Delay-based controllers have as their main advantages the simplicity with which control laws are designed and, as a consequence, their practical implementation facility. Common applications of such controllers focus mainly on second-order systems, e.g., regulation problems of DC servomotors [18,31], haptic virtual systems [20], underactuated mechanical system [32], and numerous academic examples. In the present proposal, a more challenging implementation is addressed: a flexible joint robotic arm (fourth order system), where trajectory tracking tasks are addressed.…”