Phase Margin Constraints Research Articles

DC-Link Capacitance Reduction in PFC Rectifiers Employing PI+Notch Voltage Controllers

It is well-known that adding a notch filter in series with the typically employed type-II (or PI) regulator allows improving the tradeoff between dc-link voltage dynamics and grid-side current total harmonic distortion (THD) in practical single-phase power factor correction rectifiers. The article demonstrates that notch filter utilization alternatively allows reducing the value of dc-link capacitance in case hold-up time requirement is absent. The revealed value of minimum capacitance is expressed by explicit function of possible mains frequency values range, maximum expected grid voltage magnitude, rated system power, dc-link voltage set point, maximum tolerable grid-side current THD, and the desired phase margin (PM) of dc-link voltage loop. It is demonstrated that the proposed approach yields fourfold reduction of dc-link capacitance for typical values of 5% tolerable grid-side current THD under 40° PM constraint. Experimental results exhibit close-fitting resemblance to corresponding analytical predictions, verifying the proposed methodology.

Stabilisation of network-controlled aircraft pitch control system with time delay

This paper describes the stability assurance of network-controlled aircraft pitch control system with time delays. A frequency-domain method is used to determine the upper bound of time delay for aircraft pitch control system with gain and phase margin constraint. The effectiveness of proportional-integral (PI) and fractional-order PI controller on aircraft pitch control system stability and performance is investigated in presence of time delay. The parametric space of the PI and fractional-order PI controller are plotted in two-dimensional space to determine the stability region and controller is designed with concern to the time delay. The relation between controller parameters and time delay is estimated and these findings contribute significantly for the design of the controller for aircraft pitch control system. The accuracy of the proposed results is validated using simulation benchmark.

An Analytic Interpolation Approach to Stability Margins With Emphasis on Time Delay

Unlike the situation with gain and phase margins in robust stabilization, the problem to determine an exact maximum delay margin is still an open problem, although extensive work has been done to establish upper and lower bounds. The problem is that the corresponding constraints in the Nyquist plot are frequency dependent, and encircling the point <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$s=-1$</tex-math></inline-formula> has to be done at sufficiently low frequencies, as the possibility to do so closes at higher frequencies. In this article, we present a new method for determining a sharper lower bound by introducing a frequency-dependent shift. The problem of finding such a bound simultaneously with gain and phase margin constraints is also considered. In all these problems, we take an analytic interpolation approach.

Autopilot Structured H∞ Synthesis for Satisfying Gain and Phase Margin Constraints

Aiming at the static unstable Hypersonic vehicle, a method for designing H∞ autopilot to satisfy gain margin and phase margin is proposed. Structured H∞ synthesis is used to synthesize the autopilot under the fixed structure. The gain margin and phase margin were constrained by using H∞ norm of the complementary of the scaled plant. The requirement for the gain margin and phase margin is represented by the distance between the open loop Nyquist curve and the circle that represents the gain margin and phase margin in the complex plane. The distance is adjusted by tuning the parameter of performance specifications automatically to reduce the conservatism of the controller. The present method is applicable to both static stable vehicle and static unstable vehicle, and a three loops acceleration tracking autopilot is design. The numerical simulations have demonstrated that the autopilot satisfys the performance specifications, gain margin and phase margin simultaneously.

Phase Margin Oriented Design and Analysis of UDE-Based Controllers Under Actuator Constraints

A loop compensator design for power electronic converters is typically phase margin oriented due to widely varying operation point and actuator delay. The former challenge has been successfully treated recently by uncertainty and disturbance estimator (UDE) based controllers owing to their two-degrees-of-freedom nature, allowing nearly independent tuning of tracking and disturbance rejection performance. On the other hand, actuator-imposed constraints have not been discussed in UDE-related literature by far. It is well known that in order to fully utilize the available control bandwidth, actuator dynamics must be taken into consideration. Consequently, this paper reveals guidelines for UDE-based controllers design considering typical actuator dynamics under phase margin constraint, set a priori. The proposed method is then applied to power control of a multimode bidirectional noninverting buck-boost converter, connecting two dc microgrids. Simulations and experimental results are given to support the revealed findings.

Satisfaction of gain and phase margin constraints using proportional controllers

Gain and phase margins (GM and PM) are frequently used as robustness indicators for linear time invariant systems. In many cases, the design problem is reduced to determination of a loop gain to satisfy several design criteria including gain and PM specifications. Therefore finding the set of fixed order compensators that satisfy given gain and PM specifications attracted the attention of a considerable part of the scientific community recently. It is possible to show that it may not be possible to satisfy the required gain and/or PM specifications using only a proportional controller. As a result, finding the limits of the proportional controllers for a given plant (i.e. finding the maximum achievable gain and PMs, MAGM and MAPM) is also important. After providing alternative methods (to those that already exist in the literature) for determining all stabilising proportional controllers that satisfy gain and PM constraints, a new method for calculating MAGM and MAPM using proportional controllers is given in this article. A formulation to calculate maximum gain that results in MAGM is also provided.

Robust Performance Limitations and Design of Controlled Delayed Systems

This paper presents performance limitations and a control design methodology for nonminimum phase plants of the pure delay type subject to robustness constraints. Of interest is the design of a set of controllers, for which the open-loop transfer function is a proportional-integral (PI) controller plus delay, meeting constraints on the magnitude of the closed-loop transfer function and on the plant gain uncertainty. These two specifications are used to characterize the robustness, and are a recommended alternative to the gain and phase margin constraints. A control design plot is presented which allows for selection of controller parameters including those for the lowest sensitivity controller, and graphically highlights gain and phase margin tradeoffs. The paper discusses limitations of performance of such systems in terms of crossover frequency and sensitivity. In addition, expressions and design plots are provided for a simplified approximate solution.