Open-loop Poles Research Articles

Mechanisms of middle-frequency oscillations in an offshore wind farm induced by the converter current inner loops

Abstract Middle-frequency oscillation instability is one of the important issues that threats the safe integration of offshore wind farms. However, analytical explanations to key affecting factors and laws for the middle-frequency oscillation are not clear yet, which makes it difficult to avoid this kind of oscillation effectively. Therefore, in this paper, mechanism for the middle-frequency oscillation induced by the dynamics of converter current inner loops is studied in-depth. First, small-signal transfer function model for a general offshore wind farm integrated via AC submarine cable is established. Then impact of the AC submarine cable and control parameters of the converter current inner loops on oscillation stability of the wind farm is analysed via eigenvalue analysis. It is found that with the length of AC submarine cable increases, frequency for the open-loop pole of the AC grid decreases. When open-loop pole of the AC grid gets close that of the PMSGs on complex plane, the near strong mode resonance can cause middle-frequency oscillation of the system. Finally, effectiveness of the conclusions drawn is evaluated through nonlinear simulations.

Two-port feedback analysis on Miller-compensated amplifiers

In this paper, various Miller-compensated amplifiers are analyzed by using the two-port feedback analysis together with the root-locus diagram. The proposed analysis solves problems of Miller theorem/approximation that fail to predict a pole-splitting and that require an impractical assumption that an initial lower frequency pole before connecting a Miller capacitor in a two-stage amplifier should be associated with the input of the amplifier. Since the proposed analysis sheds light on how the closed-loop poles originate from the open-loop poles in the s-plane, it allows the association of the closed-loop poles with the circuit components and thus provides a design insight for frequency compensation. The circuits analyzed are two-stage Miller-compensated amplifiers with and without a current buffer and a three-stage nested Miller-compensated amplifier.

Bode Integral Limitation For Irrational Systems

Bode integrals of sensitivity and sensitivity-like functions along with complementary sensitivity and complementary sensitivity-like functions are conventionally used for describing performance limitations of a feedback control system. In this paper, we investigate the Bode integral and evaluate what happens when a fractional order Proportional-Integral-Derivative (PID) controller is used in a feedback control system. We extend our analysis to when fractal PID controllers are applied to irrational systems. We split this into two cases: when the sequence of infinitely many right half plane open-loop poles doesn't have any limit points and when it does have a limit point. In both cases, we prove that the structure of the Bode Integral is analogous to the classical version under certain conditions of convergence. We also provide a sufficient condition for the controller to lower the Bode sensitivity integral.

A New Type of Weak Grid IBR Oscillations

This letter presents the discovery of a new type oscillations associated with inverter-based resources (IBRs) in weak grids. While typical weak grid oscillations become worse when the grid strength decreases and the power exporting level increases, this new type of oscillations appear when the grid becomes weaker and the power exporting level decreases. Electromagnetic transient (EMT) simulation results are presented, along with eigenvalue loci for a varying power. The notable signatures of such oscillations are also remarked. In further analysis, a feedback system consisting of two blocks is derived with one block associated with the phase-locked-loop (PLL) and the other associated with the rest of the system. This feedback system quantitatively demonstrates why insufficient damping in the PLL may be an issue for stability. Open-loop analysis shows that a larger phase lag in angle tracking in the low-frequency range due to high power exporting level at the weak grid condition is beneficial to the open-loop poles introduced by the PLL. And this is the reason why such oscillations may appear when power is ramping down.

Robust Control Performance for Open Quantum Systems

Robust performance of control schemes for open quantum systems is investigated under classical uncertainties in the generators of the dynamics and nonclassical uncertainties due to decoherence and initial state preparation errors. A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error to the quantum state error. This makes it possible to apply tools from classical robust control, such as structured singular value analysis. A difficulty arising from the singularity of the closed-loop Bloch equations for the quantum state is overcome by introducing the #-inversion lemma, a specialized version of the matrix inversion lemma. Under some conditions, this guarantees continuity of the structured singular value at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$s = 0$</tex-math></inline-formula> . Additional difficulties occur when symmetry gives rise to multiple open-loop poles, which under symmetry-breaking unfold into single eigenvalues. The concepts are applied to systems subject to pure decoherence and a general dissipative system example of two qubits in a leaky cavity under laser driving fields and spontaneous emission. A nonclassical performance index, steady-state entanglement quantified by the concurrence, a nonlinear function of the system state, is introduced. Simulations confirm a conflict between entanglement, its log-sensitivity and stability margin under decoherence.

Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles

In this paper, a new method to manage the stabilization and control problems of n-dimensional linear systems plus dead time, which includes one, two, or three unstable poles, is proposed. The control methodology proposed in this work is an Observer-based Proportional-Integral-Derivative (PID) strategy, where an observer and a PID controller are used to relocate the original unstable open-loop poles to stabilize the resultant closed-loop system. The observer provides an adequate estimation of the delayed-free variables and the PID uses the delay-free variables estimated by the proposed observer. Also, step-tracking is achieved in the overall control scheme. Necessary and sufficient conditions are presented to ensure closed-loop stability based on the open loop parameters of the system. The observer-based PID strategy considers five to seven constant parameters to obtain a stable closed-loop system. A general procedure to implement the proposed control strategy is presented and its performance is evaluated by means of numerical simulations.

Ballbeam System Analysis and Design Based on Root Locus Correction and State Space Correction

The ballbeam control system is one of the most perfect and classic experimental equipment for the research and analysis of automatic control theory. Other nonlinear and unstable systems have important dynamic performance, but because the ball bar system is nonlinear and unstable, it is necessary to design a controller to correct it. In this paper, the root locus and the state space theory are used for correction. In the root locus correction, the curve of the root locus is changed by adding open-loop zeros and poles to make the system stable; in the state space, a state feedback observer is designed by using the principle of pole assignment, and the state feedback matrix K is obtained to make the system stable. Using the visual tool Simulink in MATLAB to simulate, we can see the specific control effect of the controller intuitively. The real-time control was carried out on gbb2004, and the results were observed.

Open-loop resonant poles and zeros: Frequency and time domain implications for feedback systems

Open-loop poles on, or near, the imaginary axis in the complex plane are a common occurrence in feedback systems. They can occur as part of the model in systems containing lightly damped resonances or they can be deliberately introduced so as to ensure perfect tracking for sinusoidal or periodic signals. This paper establishes both time and frequency domain implications of such poles on system performance. Dual results for zeros on, or near, the imaginary axis are also discussed. Many practitioners are, at least heuristically, aware of the broad implications of these results but, to the best of the authors’ knowledge, they have not previously been explicitly articulated nor quantified.

Rotating characteristics and stability analysis of unsymmetrical magnetically suspended motor

The rotating characteristic and the stability analysis of unsymmetrical magnetically suspended motor (MSM) are investigated in the article. Firstly, the dynamic functions of unsymmetrical MSM with different moment of inertia ratios and suspension span ratios are developed. Based on the equation of radial rotation, the open-loop pole and the frequency response are analyzed, so relationships among critical whirling frequency, moment of inertia ratio and suspension span ratio are established. Moreover, relationships among rotating characteristic, moment of inertia ratio and suspension span ratio are investigated, and then the rotation stability criterion of unsymmetrical MSM based on dual-frequency bode diagram is developed. Finally, the results prove that the proposed rotation analysis method is a potential way to analyze rotating characteristic of unsymmetrical MSM.

Application of a novel PIPDF controller in an improved plug-in electric vehicle integrated power system for AGC operation

Previously linearised plug-in electric vehicle (PEV) models are adopted in automatic generation control functioning. However, lesser attention is given towards the exact designing of a PEV unit contemplating the suitable model parameters. Therefore, this paper presents a novel approach for determining the PEV model parameters employing a Bode plot analysis in the primary frequency control operation. Furthermore, a novel proportional–integral internal proportional-derivative feedback controller is proposed for the secondary frequency control application asserting zero frequency and tie-line power deviations under steady-state condition. The proposed controller provides better dynamic stability compared to the existing controllers by adjusting open loop poles of the system. The moth flame optimisation technique is used to tune the gain parameters of the proposed controller. Simulation results, obtained from the case studies under different power scenarios, depict a significant improvement in the dynamic responses of frequency and tie-line power deviations in the presence of the proposed PEV model and optimised controller.

A Memoryless Delay-Adaptive Feedback Law for the Regulation of Discrete-Time Linear Systems

It is challenging to regulate a linear system with input delay when the delay information is absent. A solution is proposed in this paper to regulate the class of discrete-time linear systems whose open loop poles are located inside or on the unit circle. With the delay below an established upper bound, a memoryless delay-adaptive feedback design achieves the convergence of the system state and input to zero as time approaches infinity. In the event that the system has all its open loop poles strictly inside the unit circle or at $z=1$, regulation is achieved for any, arbitrarily large, bounded delay without resorting to any knowledge of the delay. The proposed delay-adaptive control design utilizes only the state at the current time instant for feedback, resulting in a memoryless feedback law convenient for implementation.

A range-extender engine speed control strategy with generator torque as an auxiliary input

For the engine speed control in a range extender, responsiveness and anti-disturbance ability of the engine speed system are limited due to the inherent delay and slow response of the engine torque. In order to improve the system performance, a speed control strategy is proposed with the generator torque as an auxiliary input besides the engine torque. Firstly, an engine load compensation is presented to decouple the response from the required generator torque to the engine speed. In addition, a parameterization controller with an anti-windup strategy is provided to control the engine speed; the robustness and stability of the system are also analyzed. Then the undesired open-loop pole of the system is reconfigured using the generator torque as a secondary input to improve the anti-disturbance performance of the system. And the actual generator torque is designed to converge to the required torque when the engine is stable at the required speed to satisfy the power requirement of the vehicle. The effectiveness and practicability of the proposed strategy are evaluated by simulations on Matlab/Simulink and experiments on a range extender.

Current Control of LCL-Type Shunt APFs: Damping Characteristics, Stability Analysis, and Robust Design Against Grid Impedance Variation

This article is focused on a dual-loop current control (grid current loop and inverter-side current loop) with the point of common coupling (PCC) voltage feedforward control for digitally controlled LCL-type shunt active power filters (APFs). However, both inverter-side current feedback and PCC voltage feedforward introduce active damping (AD) effects on different LCL elements, leading to uncertain system damping characteristics and robustness against grid impedance variation. To address this issue, the accurate system damping characteristics are evaluated through open-loop pole analysis, and the benchmarking of system stability and robustness is revealed with respect to various control and system parameters. Moreover, the system instability may occur under a large grid impedance due to high-frequency resonant units of current controllers, and an improved PCC voltage feedforward control is presented to avoid this problem. Based on these findings, a robust design procedure is proposed to obtain proper control parameters and enhance system stability and robustness. Experimental results on a 30-kVA APF prototype have finally validated the correctness and effectiveness of the proposed analysis and method.

Hybrid Integrator-Gain Systems: A Remedy for Overshoot Limitations in Linear Control?

This letter shows that for a single-input single-output linear time-invariant plant having a real unstable open-loop pole, the overshoot inherent when using any stabilizing linear time-invariant feedback controller can be eliminated with a hybrid integrator-gain-based control strategy. Key design considerations underlying the presented controller are discussed, and an interpretation of the working mechanism is provided.

Robust AD for LCL‐type grid‐connected inverter with capacitor current quasi‐integral feedback

Considering the time delay introduced by the digital control, it turns out that capacitor current proportional feedback active damping (AD) is equivalent to a frequency-dependent virtual impedance in parallel with the filter capacitor. Unstable open-loop poles will arise due to the presence of virtual negative resistor, which causes that the system stability is highly sensitive to grid-impedance variation. Therefore, this study proposes a novel capacitor current quasi-integral feedback AD method. Theoretical analysis shows the proposed AD method can extend the region of the virtual positive resistor, i.e. damping region to the half of sampling frequency (f s/2). Hence, strong robustness against the grid-impedance variation is achieved. Finally, experimental results including the proposed AD method as well as capacitor current proportional feedback AD method are given and compared, which validates the superior damping performance of the proposed scheme.

Receptance-based robust eigenstructure assignment

The robustness of receptance-based active control techniques to uncertain parameters in fitted transfer function matrices is considered. Variability in assigned closed-loop poles, which arises from uncertain open-loop poles, zeros, and scaling parameters, is quantified by means of analytical sensitivity formulae, which are derived in this research. The sensitivity formulae are shown to be computationally efficient, even for a large number of random parameters, and require only measured receptances, thereby preserving the model-free superiority of receptance-based techniques. An evolution-based global optimisation procedure is used to perform eigenstructure assignment so that the robustness, as defined by a metric, is maximised. The robustness metric is designed to scale the relative importance of each closed-loop pole and their respective real and imaginary parts. The proposed technique is tested numerically on a multi-degree-of-freedom system. It is shown that, in both single- and multiple-input systems, it is possible to increase the robustness by optimally selecting a set of closed-loop poles. However, it is determined that the closed-loop eigenvectors of the system play a significant role in the propagation of uncertainty and hence, since multiple-input systems may independently assign both closed-loop poles and eigenvectors, multiple-input systems are able to reduce the uncertainty propagation to a greater extent.

Consensus of Multiagent Systems With Time-Varying Input Delay via Truncated Predictor Feedback

This article investigates the consensus tracking of exponentially unstable multiagent systems with time-varying input delay. The truncated predictor feedback approach is utilized for designing delay-dependent state and output feedback protocols. And the explicit conditions that can realize consensus tracking are established in terms of parametric Lyapunov equations and scalar inequalities. Besides, the protocol design algorithms under the maximum allowable delay and the maximum convergence rate are, respectively, provided. Compared with the existing results, the salient characteristic of the current results is to reveal the quantitative relationship among the time delay, unstable plant, network topologies, and the convergence rate. Specifically, for achieving the consensus tracking, the synchronization force from network connectivity needs to dominate the anti-synchronization force from unstable open-loop poles and input delays; the maximum allowable input delay is inversely proportional to the sum of the unstable open-loop poles; the convergence rate becomes smaller as the input delay bounds or/and the sum of the unstable poles in plant increase. Numerical simulations confirm the effectiveness of the proposed theoretical design.

Reset control approximates complex order transfer functions

A controller with the frequency response of a complex order derivative may have a gain that decreases with frequency, while the phase increases. This behaviour may be desirable to ensure simultaneous rejection of high-frequency noise and robustness to variations of the open-loop gain. Implementations of such complex order controllers found in the literature are unsatisfactory for several reasons: the desired behaviour of the gain may be difficult or impossible to obtain, or non-minimum phase zeros may appear, or even unstable open-loop poles. We propose an alternative nonlinear approximation, combining a CRONE approximation of a fractional derivative with reset control, which does not suffer from these problems. An experimental proof of concept confirms the good results of this approximation and shows that nonlinear effects do not preclude the desired performance.

Regulation of Linear Input Delayed Systems without Delay Knowledge

In this paper, we propose a delay independent control scheme that regulates to zero the state and the control input of a linear input delayed system whose open loop poles are at the origin or in th...

Time-varying low gain feedback for linear systems with unknown input delay

In this paper, the traditional low gain feedback design with a time-invariant feedback parameter is generalized to time-varying parameter design for linear systems with delayed input. For an unknown delay with a known upper bound, a time-varying low gain feedback law, constructed by using the parametric Lyapunov equation based approach, globally regulates a system with all open loop poles at the origin as long as the time-varying low gain parameter has a continuous second derivative and approaches a sufficiently small constant with its derivative approaching zero as time goes to infinity. Improvement of the closed-loop performance is addressed in a convergence rate analysis and then observed in simulation compared with the traditional constant parameter low gain design.