By Fabricio Garelli
Presents a unified virtually oriented remedy to many limited regulate paradigms-Helps to minimize the space among the to be had limited keep watch over literature and commercial functions. Contents: Constraints in suggestions structures. facing constraints in SISO regulate. a few functional case reviews. correct instruments for dynamic decoupling. limited dynamic decoupling. bettering decoupling in decentralised regulate. Partial decoupling and non-minimum section structures. MIMO bumpless move.
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Extra resources for Advanced Control for Constrained Processes and Systems
11(a) shows the smooth convergence of x2 to its bound at x 2 ¼ 20 with the fast sliding dynamics. 11(c) displays the associated system trajectory in the phase plane (x2, x_2). The SMRC protection acts along the line t1 À t2. Obviously, the slope of the sliding surface, as well as the sliding dynamics, is given by the sliding gain k1. Once the system trajectory points towards the safety region from both sides of the sliding surface, the system naturally evolves within this region without reference conditioning towards its equilibrium point.
On the one hand, it could be designed u ¼ 0 so that the system evolves autonomously throughout the interior of F. e. when the state trajectory reaches the border @F trying to leave the set F. e. the process is driven towards its critical constraint, and then to remain on it. 43), the SMRC approach adopts the former strategy. However, there are no limitations to adopt other switching criteria, as can be seen for instance in the robotic application in Chapter 3. 5)) can be seen as making the set F invariant by means of the following law for each limiting function ( s or s): ( u¼ uþ if fðvÞ > 0 0 if fðvÞ 0 with uþ 6¼ 0 ð2:69Þ This aims to satisfy ( f_ ðxs ; uÞ ¼ Lf f þ Lg fuþ < 0 if fðvÞ > 0 Lf f > 0 if fðvÞ < 0 ð2:70Þ locally around @F, so that a sliding regime is established on surface @F.
To this end, some basics about VSS and sliding regimes are presented first. Then, they are employed for the analysis of the SMRC algorithm when dealing with biproper constrained subsystems and to gain insight into the method properties. 1 VSS essentials A VSS is a dynamical system composed of various continuous subsystems with a switching logic. In a VSS, the system structure is intentionally changed with, among others, the following objectives: ● ● ● To improve closed-loop performance. To solve control problems that continuous control is not able to work out.