Dynamics and stability of controlled systems.
This paper also contains a discussion of the theoretical behavior of the controlled system as well as comparisons of the predictions of a mathematical model with experimental results.
We employ signal temporal logic to specify the desired behavior of the controlled system once an overflow occurs and encode this behavior as constraints so that the synthesized controller reacts in time to decrease and eliminate the overflow.
The results show that the dynamic behavior of a controlled system can be changed by choosing appropriate control parameters.
Both a deeper insight in the global behavior of the controlled system and valuable design criteria are obtained.
Figure 3 3-D computer simulation result shows simple dynamical behaviors of the uncontrolled system ( 4 ) in the ( u 1, u 2, u 3 ) space for k = 2. Figure 4 3-D computer simulation result shows complex dynamical behaviors of the controlled system ( 5 ) in the ( u 1, u 2, u 3 ) space for k = 2, β = 10, γ 1 = 2 π + arcsin 1 20, γ 2 = arcsin 1 40, γ 3 = arcsin 1 60.
This paper deals with dynamical behavior and controlled system of a feed-flow-reversal in a RO desalination system, giving inspirations to effective water treatment under large uncertainties, disturbances, and noises.
Computer simulations of the controlled systems show complex dynamical behaviors such as jump phenomenon, Sommerfeld effect, period-nT and chaotic oscillations.
Figure 4 Behavior and phase portrait of a controlled system ( 1.3 ) with (pmb{tau_{1} = 0.8 > tau_{1}^{0}}), (pmb{tau_{2} = 3.0}), the Hopf bifurcation disappears.
Figure 3 Behavior and phase portrait of a controlled system ( 1.3 ) with (pmb{tau_{1} = 0}), (pmb{tau_{2} = 3.7 > tau_{2}^{0}}), the Hopf bifurcation disappears.
