scholarly journals Stability Analysis of Parameter Varying Genetic Toggle Switches Using Koopman Operators

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3133
Author(s):  
Jamiree Harrison ◽  
Enoch Yeung
Keyword(s):  
Control Strategy ◽  
Nonlinear Models ◽  
Growth Conditions ◽  
Necessary Condition ◽  
Toggle Switch ◽  
Time Varying ◽  
Genetic Circuits ◽  
Koopman Operator ◽  
Kinetic Rates ◽  
Parameter Varying

The genetic toggle switch is a well known model in synthetic biology that represents the dynamic interactions between two genes that repress each other. The mathematical models for the genetic toggle switch that currently exist have been useful in describing circuit dynamics in rapidly dividing cells, assuming fixed or time-invariant kinetic rates. There is a growing interest in being able to model and extend synthetic biological function for growth conditions such as stationary phase or during nutrient starvation. As cells transition from one growth phase to another, kinetic rates become time-varying parameters. In this paper, we propose a novel class of parameter varying nonlinear models that can be used to describe the dynamics of genetic circuits, including the toggle switch, as they transition from different phases of growth. We show that there exists unique solutions for this class of systems, as well as for a class of systems that incorporates the microbial phenomena of quorum sensing. Further, we show that the domain of these systems, which is the positive orthant, is positively invariant. We also showcase a theoretical control strategy for these systems that would grant asymptotic monostability of a desired fixed point. We then take the general form of these systems and analyze their stability properties through the framework of time-varying Koopman operator theory. A necessary condition for asymptotic stability is also provided as well as a sufficient condition for instability. A Koopman control strategy for the system is also proposed, as well as an analogous discrete time-varying Koopman framework for applications with regularly sampled measurements.

scholarly journals Fault-Tolerant Control Strategy with Asymmetric Phase Currents for Single to Four-Phase Open-Circuit Faults of Six-Phase PMSM

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3163
Author(s):  
Chen Huang ◽  
Lidan Zhou ◽  
Zujia Cao ◽  
Gang Yao
Keyword(s):  
Working Conditions ◽  
Control Strategy ◽  
Fault Tolerant ◽  
Fault Tolerant Control ◽  
Open Circuit ◽  
Time Varying ◽  
Electromagnetic Torque ◽  
Control Loops ◽  
Phase Current ◽  
Multi Phase

Multi-phase motors and generators are regarded with great fault tolerance capability, especially on open-circuit faults. Various mathematics analytical methods are applied for their fault control. In this paper, a fault-tolerant control strategy with asymmetric phase current for the open-circuit faults with arbitrary phases in the six-phase PMSM (six-phase permanent magnetic synchronous motor, 6P-PMSM) system, is proposed for better electrical and dynamical performance of the machine. An innovative mathematical model for PMSM under one to four-phase-open circuit faults are established considering the asymmetry of the machine. Combining with time-varying relations in machines’ working conditions, targeted decoupling transformation matrixes of every kind of open-circuit faults are settled by voltage equations under different faults. Modified control strategy with a connection between the neutral point and the inverter’s DC side is presented, which aims at increasing the system redundancy and reducing the amplitude of phase currents. Besides, improved control loops with two layers are put forward as well, with which the PMSM system acquires fewer harmonics in phase current and smoother electromagnetic torque. Simulation and experimental results of open-circuit faults are provided for verification of the theoretical analysis.

Optimal Control of a Flexible Mechanism Using a Combined Feedforward-Feedback Strategy: Simulation and Experiment

1999 ◽  
Author(s):  
Hubertus v. Stein ◽  
Heinz Ulbrich
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
System Performance ◽  
High Speed ◽  
Time Varying ◽  
Linkage Mechanism ◽  
Additional Degree ◽  
Control Approach ◽  
Feedback Optimal Control ◽  
Four Bar Linkage

Abstract Due to the elasticity of the links in modern high speed mechanisms, increasing operating speeds often lead to undesirable vibrations, which may render a required accuracy unattainable or, even worse, lead to a failure of the whole process. The dynamic effects e.g. may lead to intolerable deviations from the reference path or even to the instability of the system. Instead of suppressing the vibration by a stiffer design, active control methods may greatly improve the system performance and lead the way to a reduction of the mechanism’s weight. We investigate a four-bar-linkage mechanism and show that by introducing an additional degree of freedom for a controlled actuator and providing a suitable control strategy, the dynamically induced inaccuracies can be substantially reduced. The modelling of the four-bar-linkage mechanism as a hybrid multi body system and the modelling of the complete system (including the actuator) is briefly explained. From the combined feedforward-feedback optimal control approach presented in (v. Stein, Ulbrich, 1998) a time-varying output control law is derived that leads to a very good system performance for this linear discrete time-varying system. The experimental results show the effectiveness of the applied control strategy.

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