Calculation of all gains providing time-delay independent stability via root locus

Nesimioğlu, Barış Samim; Söylemez, Mehmet Turan

doi:10.1109/codit.2014.6996957

Cited by 4 publications

(4 citation statements)

References 17 publications

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“…In that case, the stability is not affected by time delay, ie if the delay-free plant is stable (unstable), then the time-delay system is stable(unstable) for all values of L. This fact is discussed in detail in [42].…”

Section: Preliminariesmentioning

confidence: 90%

“…It is worth noting that if has no positive real roots, an interesting phenomenon occurs: it is impossible for any pair of roots of to cross the imaginary axis. In that case, the stability is not affected by time delay , ie if the delay‐free plant is stable (unstable), then the time‐delay system is stable(unstable) for all values of L. This fact is discussed in detail in .…”

Section: Preliminariesmentioning

confidence: 99%

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All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

Nesimioğlu

Söylemez

2016

Asian Journal of Control

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In this paper, a simple derivation for an all-stabilizing proportional controller set for first-order bi-proper systems with time delay is proposed. In contrast to proper systems, an extremely limited number of studies are available in the literature for such bi-proper systems. To fill this gap in the literature, broader aspects of the stabilizing set are taken into consideration. The effect of zero on the stabilizing set is clearly discussed and we also prove that, when their zeros are placed symmetrically to the origin, the stabilizing set of non-minimum phase plant is always smaller than that of the minimum phase one. Moreover, for an open-loop unstable plant, maximum allowable time delay (MATD) is explicitly expressed as a function of the locations of the pole and zero. From that function, it is shown that for a minimum phase plant, the supremum of the MATD is two times that of the time constant of the plant and the infimum of the MATD is the time constant of the plant. We also prove that the supremum is the time constant and the infimum is zero for a non-minimum phase plant.

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Section: Preliminariesmentioning

confidence: 90%

Section: Preliminariesmentioning

confidence: 99%

All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

Nesimioğlu

Söylemez

2016

Asian Journal of Control

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“…Various control methods have been proposed to compensate the time delay [10]- [12]. In [13], [14], the predictive deadbeat control is proposed to compensate the time delay.…”

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confidence: 99%

Multisampling Method for Single-Phase Grid-Connected Cascaded H-Bridge Inverters

Wang

Blaabjerg

et al. 2020

IEEE Trans. Ind. Electron.

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This paper proposes a multi-sampling method for single-phase grid-connected cascaded H-bridge (CHB) multilevel inverters with the phase-shifted carrier pulsewidth modulation (PSC-PWM) in order to reduce the time delay involved in the control loop and increase the control bandwidth. In this method, the controlled variables are sampled not only at the peak and the valley of all triangular carriers, but also at the intersection points of all phase-shifted carriers and inverted ones, which enables a minimum unity sampling interval without detecting the current ripple caused by the switching action and breaking the voltage-second balance in the modulation process. The bandwidth of the current control loop based on the proposed sampling method is illustrated and compared to other traditional sampling methods. The analysis shows that the system effectively reduces the time delay involved in the control loop and improves the bandwidth of the control loop. Finally, a downscale test platform of the single-phase grid-connected CHB multilevel inverter with an inductance (L)-filter is built to verify the effectiveness of the proposed method.

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“…To address this problem, in [17], an effective and simple methodology to compute all P type controllers providing timedelay independent stability is given for SISO-LTI systems. Although there are some methods about delay-independent stability available in the literature [18][19][20], the method given in [17] is much easy to understand and provides a simple and fast solution for the SISO LTI plants. The methodology is based on the stability analysis given in [9] and it consists of forming the magnitude polynomial, sketching the resulting root locus with the suitable transformations of the variables and searching the regions of gains for which any positive real roots do not exist.…”

Section: Introductionmentioning

confidence: 99%

Robust Stabilization of a Servomechanism With Respect To Time-Delay

Nesimioğlu

Yılmaz

Dincel³

2016

International Journal of Applied Mathematics, Electronics and Computers

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Abstract:In this paper, a servomechanism under teleoperation is considered. Since the teleoperation itself can result in large amount of time-delays and this amount can change operation to operation, it can be difficult to control such mechanisms in order to accomplish the desired tasks. From the robust control viewpoint, a methodology that guarantees the stability in worst case is essential. Based on a simple methodology to find the delay independent stabilizing proportional (P) controller regions, just by forming the magnitude polynomial and employing the root locus technique, the stability of the robot is guaranteed, even in the worst case: the system becomes stable even if the connection has huge amount of time-delays. This fact is evidenced first by the simulations. To simulate the real system, as there is no information about the motor parameters, the motor is modeled by a global optimization methodology, named Genetic Algorithm in order to obtain a valid model for the system as accurate as possible. Then the resulting P controllers are applied to the real system, the results of which are found in accordance with the simulation results; the stability of the operation is not affected by the time-delay.

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Calculation of all gains providing time-delay independent stability via root locus

Cited by 4 publications

References 17 publications

All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

All‐Stabilizing Proportional Controllers for First‐Order Bi‐Proper Systems with Time Delay: An Analytical Derivation

Multisampling Method for Single-Phase Grid-Connected Cascaded H-Bridge Inverters

Robust Stabilization of a Servomechanism With Respect To Time-Delay

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