Effect of fractional-order PID controller with acceleration feedback on a linear single degree-of-freedom oscillator

A linear single degree-of-freedom (SDOF) oscillator with fractional-order PID controller of acceleration feedback is investigated by the averaging method, and the approximately analytical solution is obtained. Moreover, the numerical solution of the system is obtained by the step-down order method and the power series method progressively. The effects of the parameters in fractional-order PID controller on the dynamical properties are characterized by some new equivalent parameters. The proportional component of fractional-order PID controller is characterized in the form of equivalent mass. The integral component of fractional-order PID controller is denoted in the form of the equivalent linear damping and equivalent mass. The differential component of fractional-order PID controller is denoted in the form of the equivalent linear negative damping and equivalent mass. Those equivalent parameters could distinctly illustrate the effects of the parameters in fractional PID controller on the dynamical response. A comparison between the analytical solution with the numerical results is made, and their satisfactory agreement verifies the correctness of the approximately analytical results. The effects of the parameters in fractional-order PID controller on control performance are further analyzed by some performance parameters of the time response. Finally, the robustness of the fractional-order PID controller based on acceleration feedback is demonstrated through the control of a SDOF quarter vehicle suspension model

Effect of fractional-order PID controller with acceleration feedback on a linear single degree-of-freedom oscillator

A linear single degree-of-freedom (SDOF) oscillator with fractional-order PID controller of acceleration feedback is investigated by the averaging method, and the approximately analytical solution is obtained. Moreover, the numerical solution of the system is obtained by the step-down order method and the power series method progressively. The effects of the parameters in fractional-order PID controller on the dynamical properties are characterized by some new equivalent parameters. The proportional component of fractional-order PID controller is characterized in the form of equivalent mass. The integral component of fractional-order PID controller is denoted in the form of the equivalent linear damping and equivalent mass. The differential component of fractional-order PID controller is denoted in the form of the equivalent linear negative damping and equivalent mass. Those equivalent parameters could distinctly illustrate the effects of the parameters in fractional PID controller on the dynamical response. A comparison between the analytical solution with the numerical results is made, and their satisfactory agreement verifies the correctness of the approximately analytical results. The effects of the parameters in fractional-order PID controller on control performance are further analyzed by some performance parameters of the time response. Finally, the robustness of the fractional-order PID controller based on acceleration feedback is demonstrated through the control of a SDOF quarter vehicle suspension model

Effect of fractional-order PID controller with acceleration feedback on a linear single degree-of-freedom oscillator

A linear single degree-of-freedom (SDOF) oscillator with fractional-order PID controller of acceleration feedback is investigated by the averaging method, and the approximately analytical solution is obtained. Moreover, the numerical solution of the system is obtained by the step-down order method and the power series method progressively. The effects of the parameters in fractional-order PID controller on the dynamical properties are characterized by some new equivalent parameters. The proportional component of fractional-order PID controller is characterized in the form of equivalent mass. The integral component of fractional-order PID controller is denoted in the form of the equivalent linear damping and equivalent mass. The differential component of fractional-order PID controller is denoted in the form of the equivalent linear negative damping and equivalent mass. Those equivalent parameters could distinctly illustrate the effects of the parameters in fractional PID controller on the dynamical response. A comparison between the analytical solution with the numerical results is made, and their satisfactory agreement verifies the correctness of the approximately analytical results. The effects of the parameters in fractional-order PID controller on control performance are further analyzed by some performance parameters of the time response. Finally, the robustness of the fractional-order PID controller based on acceleration feedback is demonstrated through the control of a SDOF quarter vehicle suspension model

DNA duplex recognition activates Exo1 nuclease activity

Exonuclease 1 (Exo1) is an evolutionarily conserved eukaryotic nuclease that plays a multifaceted role in maintaining genome stability. The biochemical attributes of Exo1 have been extensively characterized via conventional assays. However, the key step governing its activation remains elusive. Extending the previous finding that Exo1 can digest a randomly selected single-stranded DNA (ssDNA) but not a poly(dT) oligonucleotide and using purified recombinant Exo1 and nuclease and electrophoretic mobility shift assays, here we determined that DNA hairpins with a stem size of 4 bp or longer are able to activate Exo1-mediated digestion of ssDNA. We further provide evidence suggesting that Exo1 uses an evolutionarily conserved residue, Lys¹⁸⁵. This residue interacted with the phosphate group bridging the third and fourth nucleotide on the digestion strand of the substrate DNA for duplex recognition, critical for Exo1 activation on not only ssDNA but also dsDNA. Additionally, the defect of an exo1-K185A mutant in duplex digestion was partially rescued by longer overhanging DNA. However, we noted that the enhanced Exo1 nuclease activity by longer overhanging DNA is largely eliminated by replication protein A (RPA), likely because of the previously reported RPA activity that strips Exo1 off the ssDNA. We conclude that duplex DNA contact by Exo1 is a general mechanism that controls its activation and that this mechanism is particularly important for digestion of duplex DNA whose nascent ssDNA is bound by RPA

Chaos threshold analysis of Duffing oscillator with fractional-order delayed feedback control

In this paper, the bifurcation and chaotic threshold of Duffing oscillator with fractional-order delayed feedback control is studied. The fractional-order delayed feedback control is equivalent to the approximate integer-order control. It is found that the fractional-order delayed feedback control has the function of displacement feedback and velocity feedback. Then, the analytically necessary condition for generating chaos in Duffing oscillator with fractional-order delayed feedback control is obtained by Melnikov method. The accuracy of the analytically necessary condition by Melnikov method is verified by numerical simulation and the largest Lyapunov exponents of the system. From the analysis of the numerical simulation results, it is found that there are two paths leading to the chaos after period-doubling bifurcations due to different initial values in Duffing oscillator with fractional-order delayed feedback. Finally, the influence of the parameters of the fractional-order delayed feedback control on bifurcation and chaos is analyzed. The increase of the fractional-order delayed feedback gain will resist the generation of chaos. Both time delay and the fractional-order affect the threshold of chaos in the form of trigonometric functions. The better control performance in the system can be obtained by choosing the reasonable fractional order and time delay. Those results present some new system characteristics which provide theoretic guidance to design and control of this kind system