Open-loop Function Research Articles

Stability assessment and parametric sensitivity analysis based on extended Gershgorin Theorem for multiple grid-connected converters

• A multiple grid-connected converters is modeled as a medium and high dimensional negative feedback system with a stable open-loop function in unified dq frame, which fills in the limitations of traditional impedance ratios for the small disturbance stability analysis of multiple grid-connected converters system. • In terms of estimating eigenvalues for the multiple grid-connected converters system, a stability assessment method based on extended Gershgorin Theorem is proposed in frequency domain. Moreover, the algebraic form of the criterion is further simplified to quantify the oscillatory stability, which has the lower complexity compared with generalized nyquist criterion. The proposed method is of great potential in analyzing the stability issue for large-scale new energy power systems. • The reshaped eigenvalue estimation area based on extended Gershgorin Theorem is smaller than traditional Gershgorin Theorem, which can reduce its conservatism to improve system stability margin. • Compared to observe the changed trend of system stability by the change of the related parameters, the parameter sensitivity analysis based on equivalent impedance network model is used to quantify the impact factors on stability, which can be given to guide the parameter optimization of the multiple grid-connected converters system. The large-scale integration of power electronic based systems is bringing new oscillatory stability issues, further threatening the safe and stable operation of power system. Early researches are focused on stability analysis of single grid-connected converters to simple networks. Instead, there have been growing interests in studying the small signal stability of multiple grid-connected converters nowadays, whose main method is to apply traditional stability assessment with high complexity and conservatism. To address this problem, a simplified criterion based on extended Gershgorin Theorem to assess the stability of multiple grid-connected converter. The proposed method has less conservatism than tradition Gershgorin Theorem-based criteria, and has the lower computational complexity with simple algebraic operation compared to generalized nyquist criteria. Moreover, the parametric sensitivity analysis is used for analyzing the impact factors to promote system stability based on the proposed criteria. Theoretical results as well as electromagnetic transient simulations have verified the validity. The proposed method has the potential to assess the high-order system, and provides guidance on system parameters optimization based on the sensitivity.

Stability assessment for multiple grid-connected converters based on impedance-ratio matrix and Gershgorin’s Theorem

Recent years have witnessed emerging oscillatory stability issues in power systems with high-penetration renewable and large power electronic loads. These issues are generally caused by the dynamic interaction between the AC/DC grid and power electronic converters. However, the traditional impedance analysis has some limitations to study the small disturbance stability of multiple grid-connected converters. In this paper, the system is modeled as a medium and high dimensional negative feedback system with a stable open-loop function, which the equivalent open-loop function is defined as impedance-ratio matrix. Moreover, a sufficient stability criterion based on Gershgorin’s Theorem is developed through directly estimating the possible range of eigenvalues. Finally, the validity of the criterion is verified by a 7-infeed converters system. Theoretical analysis and electromagnetic transient simulations show this criterion has the potential to assess the high-order system small disturbance stability problems with low computational complexity. Moreover, its low conservatism as a sufficient criterion is helpful to guide the parameter design for grid-connected system.

Improved series active power filter with fundamental and harmonic magnetic flux hybrid compensation

The filtering performance of series hybrid active power filter (SHAPF) based on fundamental magnetic flux compensation positively correlates with the magnetising impedance of the transformer. However, excessive magnetising impedance will decrease reliability while increasing capacity and costs of the whole system. In order to reduce the magnetising impedance while ensuring the same filtering performance of SHAPF, an improved series active power filter (ISAPF) with fundamental and harmonics magnetic flux hybrid control is presented here. The equivalent impedances to fundamental and harmonics in ISAPF are firstly analysed to explain the principle of ‘harmonic isolation’. Then the range of compensation coefficients is investigated in detail based on the complete control block diagram and the open-loop function of ISAPF. Moreover, stability conditions of an overall system with non-linear loads are deduced. Finally, a set of single-phase prototype with two kinds of special transformer has been constructed; the related experiments results showed that ISAPF can ensure the filtering performance while applying a transformer with smaller capacity, thus resulting in the reduction in capacity and the costs while increasing the reliability.

Impact of lipopolysaccharide-induced acute inflammation on baroreflex-controlled sympathetic arterial pressure regulation.

BackgroundLipopolysaccharide (LPS) induces acute inflammation, activates sympathetic nerve activity (SNA) and alters hemodynamics. Since the arterial baroreflex is a negative feedback system to stabilize arterial pressure (AP), examining the arterial baroreflex function is a prerequisite to understanding complex hemodynamics under LPS challenge. We investigated the impact of LPS-induced acute inflammation on SNA and AP regulation by performing baroreflex open-loop analysis.MethodsTen anesthetized Sprague-Dawley rats were used. Acute inflammation was induced by an intravenous injection of LPS (60 μg/kg). We isolated the carotid sinuses from the systemic circulation and controlled carotid sinus pressure (CSP) by a servo-controlled piston pump. We matched CSP to AP to establish the baroreflex closed-loop condition, whereas we decoupled CSP from AP to establish the baroreflex open-loop condition and changed CSP stepwise to evaluate the baroreflex open-loop function. We recorded splanchnic SNA and hemodynamic parameters under baroreflex open- and closed-loop conditions at baseline and at 60 and 120 min after LPS injection.ResultsIn the baroreflex closed-loop condition, SNA continued to increase after LPS injection, reaching three-fold the baseline value at 120 min (baseline: 94.7 ± 3.6 vs. 120 min: 283.9 ± 31.9 a.u.). In contrast, AP increased initially (until 75 min), then declined to the baseline level. In the baroreflex open-loop condition, LPS reset the neural arc (CSP-SNA relationship) upward to higher SNA, while shifted the peripheral arc (SNA-AP relationship) downward at 120 min after the injection. As a result, the operating point determined by the intersection between function curves of neural arc and peripheral arc showed marked sympatho-excitation without substantial changes in AP.ConclusionsLPS-induced acute inflammation markedly increased SNA via resetting of the baroreflex neural arc, and suppressed the peripheral arc. The balance between the augmented neural arc and suppressed peripheral arc determines SNA and hemodynamics in LPS-induced acute inflammation.

An open-loop approach to calculate noise-induced transitions

Bistability permits the co-existence of two distinct cell fates in a population of genetically identical cells. Noise induced transitions between two fates of a bistable system are difficult to calculate due to the intricate interplay between nonlinear dynamics and noise in bistable positive feedback loops. Here we opened multivariable feedback loops at the slowest variable to obtain the open-loop function and the fluctuations in the open-loop output. By the subsequent reclosing of the loop, we calculated the mean first passage time (MFPT) using the Fokker-Planck equation in good agreement with the exact stochastic simulation. When an external component interacts with a feedback component, it amplifies the extrinsic noise in the loop. Consequently, the open-loop function is shifted and the transition rates between the two states in the closed loop are increased. Despite this shift, the open-loop output reflects the system faithfully to predict the MFPT in the feedback loop. Therefore, the open-loop approach can help theoretical analysis. Furthermore, the measurement of the mean value, variance, and the reaction time-scale of the open-loop output permits the prediction of MFPT simply from experimental data, which underscores the practical value of the stochastic open-loop approach.

Contribution of Bistability and Noise to Cell Fate Transitions Determined by Feedback Opening

Alternative cell fates represent a form of non-genetic diversity, which can promote adaptation and functional specialization. It is difficult to predict the rate of the transition between two cell fates due to the strong effect of noise on feedback loops and missing parameters. We opened synthetic positive feedback loops experimentally to obtain open-loop functions. These functions allowed us to identify a deterministic model of bistability by bypassing noise and the requirement to resolve individual processes in the loop. Combining the open-loop function with kinetic measurements and reintroducing the measured noise, we were able to predict the transition rates for the feedback systems without parameter tuning. Noise in gene expression was the key determinant of the transition rates inside the bistable range. Transitions between two cell fates were also observed outside of the bistable range, evidenced by bimodality and hysteresis. In this case, a slow transient process was the rate-limiting step in the transitions. Thus, feedback opening is an effective approach to identify the determinants of cell fate transitions and to predict their rates.

Adaptive Hybrid Visual Servo Regulation of Mobile Robots Based on Fast Homography Decomposition

For the monocular camera-based mobile robot system, an adaptive hybrid visual servo regulation algorithm which is based on a fast homography decomposition method is proposed to drive the mobile robot to its desired position and orientation, even when object’s imaging depth and camera’s position extrinsic parameters are unknown. Firstly, the homography’s particular properties caused by mobile robot’s 2-DOF motion are taken into account to induce a fast homography decomposition method. Secondly, the homography matrix and the extracted orientation error, incorporated with the desired view’s single feature point, are utilized to form an error vector and its open-loop error function. Finally, Lyapunov-based techniques are exploited to construct an adaptive regulation control law, followed by the experimental verification. The experimental results show that the proposed fast homography decomposition method is not only simple and efficient, but also highly precise. Meanwhile, the designed control law can well enable mobile robot position and orientation regulation despite the lack of depth information and camera’s position extrinsic parameters.

Application of a dead time compensator as a PID controller

In this paper, the application of Dominant Gain Concept for controlling time delay processes is considered from a new viewpoint. In this viewpoint, time delay is considered as function with infinite Right Half Plane (RHP) zeros which are transferred to the Left Half Plane by adding a proper transfer function to the open loop function. Furthermore, by defining a new concept, called minimum-gain frequency, the propositions for control system stability and the manner of choosing order and gain of the added transfer function are proved. Also, the application of this method is studied in order to simultaneously compensate for the Right Half Plane zeros and time-delay. Finally, easy application of this method is shown in an ordinary feedback loop as a PID controller.

An Approach to Estimate Time-varying Casual Coherence Function

This paper describes the development of a model-based approach to estimating both open-loop and causal time-varying coherence functions (TVCF). Theoretical derivations of the coherence bounds using the proposed approach are also provided. A time-varying vector autoregressive (VAR) model was used to estimate both open-loop and causal TVCF. The time-varying optimal parameter search method was employed to identify the time-varying model coefficients as well as the model order of the VAR model. Simulation results revealed interesting observations, and they were corroborated using experimental renal blood pressure and flow data. Specifically, experimental data showed that in certain cases, the calculation of the open-loop TVCF might provide incorrect interpretation of the results when the system under investigation was a closed-loop system, which is consistent with theoretical derivations. The use of the closed-loop TVCF not only provides quantitative assessment of the coupling between the two signals, but it also provides valuable insights into the composition of the physical structure of the system.

Stability analysis and design of automatic frequency control system for in vivo EPR spectroscopy.

Stability analysis and design of an automatic frequency control (AFC) system for in vivo continuous-wave EPR spectroscopy is described. The open-loop function of the feedback control system for the AFC was derived and the stability of the feedback loop systematically examined. A stability analysis of the system is demonstrated and a systematic design procedure is proposed. The design is started from the required system specifications (phase margin, steady-state error, and system bandwidth) and clear guidelines for designing an AFC system are given. A case study of the design is presented based on the specific needs of in vivo EPR measurements. A phase margin of 53 degrees, a steady-state error of 1.6%, and a system bandwidth of up to 1.8 kHz were obtained in the designed AFC system. The system specifications defined in advance are satisfied in this case study.

Control of overshoot in the step response of chemical processes

The paper deals with the problem of avoiding overshoot in the closed loop response of a chemical process to a step input. Significant results relating the step response overshoot to poles and zeros of the open loop function are reviewed. Prom a general theorem relating the position of zeros and poles to the occurrence of extrema points in the step response, a direct method for the design of PID controllers, able to avoid overshoot in the closed loop response, is derived. Examples of application are reported for low order processes, for which analytical values of the controller parameters can be easily derived. Simulation results illustrate the potential of the design technique.

Chronic isolation of carotid sinus baroreceptor region in conscious normotensive and hypertensive rats.

We have developed a chronic technique to isolate the carotid sinus baroreceptor region in the conscious rat model. Our technique, when used in conjunction with other methods, allows for the study of the control of arterial pressure, heart rate, and cardiac output by the carotid sinus baroreceptor reflex in conscious, unrestrained rats. The performance of our technique was evaluated in two strains: normotensive Sprague-Dawley (SD) rats and spontaneously hypertensive rats (SHR). Each rat was instrumented with an aortic flow probe and a catheter placed in the right femoral artery to monitor cardiac output and arterial pressure, respectively. The cervical sympathetic trunk and aortic depressor nerve were ligated and cut bilaterally, leaving vagus nerves intact. The right and left carotid sinuses were isolated using our new technique. We tested the open-loop function of the carotid sinus baroreceptor reflex system in the conscious rat after recovery from the isolation surgery. We found that changes in nonpulsatile carotid sinus pressure caused significant changes in arterial pressure, heart rate, and total peripheral resistance in both rat strains. However, the cardiac output responses differed dramatically between strains. Significant changes were seen in the cardiac output response of SHR, whereas no significant changes were observed in normotensive SD rats. We have found this technique to be a highly reliable tool for the study of the carotid sinus baroreceptor reflex system in the conscious rat.

Energy minimization of vibrating plates subject to constraints on open and closed loop control forces

The undesirable vibrations of a rectangular plate are suppressed by means of a combined open-closed loop control mechanism. The closed loop control mechanism is assumed to be proportional to displacement. The energy functional of the plate is minimized within a specified period of time with respect to both the open loop function and the displacement feedback parameter. The minimization is carried out subject to constraints on the open loop control force as well as on the closed loop force. For the open loop constraint a Lagrange multiplier is used to incorporate the contraint into an augmented energy functional. An explicit solution of the open loop control problem is obtained. Numerical results are given to indicate the effectiveness of the proposed control.

Vibration damping of a thin plate by optimal open-and closed-loop control forces

The vibrations of a rectangular plate are damped out by means of a combined open-closed-loop control mechanism. A functional involving the displacement, velocity and open-loop control function is minimized with respect to both the open-loop function and the displacement feedback parameter. The minimization is carried out subject toa constraint on the amount of feedback force that can be spent in the control process. An explicit solution of the problem is obtained and the theory is applied to the vibrating damping of an impulsively loaded plate. Numerical results are given to indicate the effectiveness of the proposed control mechanism.

Control aspects of human temperature regulation

Human body temperature control is characterized by a local dependence of system variables and parameters: receptors are thought to be distributed locally throughout the body. The integrative control centres appear to extend quasicontinuously from the spinal cord up to the hypothalamus. Finally, control actions obviously affect the passive system with distinct local dependence. The essential properties of non-linear distributed parameter control of human body temperature are demonstrated by way of experimental and mathematical results. With regard to the control strategy there are evidently five different concepts which claim to answer the question: ‘What is regulated and how?’ A control concept based on spatial integration of temperatures plus local effector actuation seems to be the one which is most adequately supported by system-theoretical as well as by experimental results. The discussion about ‘reference’ and ‘set-point’ of temperature regulation is still going on, and concentrates on four concepts. The concept of balance of passive and active processes, i.e. of controlling and of controlled subsystems, defines the steady-state as the only compatible operating point of the open loop functions in the closed control loop. It does not need an explicit neuronal reference input or difference of controller inputs and solves simultaneously the so-called problem of changing set-point due to fever or to circadian rhythm. This is explained as an adjustment of control parameters requiring another balance of controller and passive system.

Root-locus Equations of the Fourth Degree†

ABSTRACT The paper is a study of the geometrical properties of root-loci for higher-order systems. Properties of general higher-plane algebraic curves are invoked to provide the broad framework of reference for systematic investigation of root-locus properties. Such an approach affords better integrated and more comprehensive understanding of the nature of the root-paths for higher-order systems. The discussion is a composite one, encompassing all T(N,M) systems of the order N + M Δ h = 5 and 6, whose equations involve fourth-degree powers in ω: N and M denote the number of poles and zeros, respectively, of the open-loop function G(S) where, S = σ + jω. The examples cited are illustrative of all significant features of higher-plane algebraic curves as manifest in root-locus shapes. Conditions for existence of such features in root-loci are examined and procedures for their identification and location established.

An analytical approach to root loci

The general algebraic equations of root loci for real <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> are found in polar and Cartesian coordinates. A synthesis method is then suggested which leads to linear equations in the coefficients of the open-loop transfer function when closed-loop poles and their corresponding gains are specified. Equations are also found for the gain corresponding to a given point on the root locus. A superposition theorem is presented which shows how the root loci for two open-loop functions place constraints on the locus for their product. With a knowledge of the simple lower-order loci, this theorem can be used in sketching and constructing root loci.

Rapid determination of approximate closed-loop poles of feedback control systems

In a control system, the transient response can be determined accurately only when the closed-loop poles of the system are known. The determination of the closed-loop poles involves in general a solution of a high-degree equation, which is difficult when the degree of the equation exceeds two. While mathematicians have attempted to solve such equations analytically, the control engineers have preferred approximate graphical solutions. The present paper suggests an extension of an already existing graphical method. The technique followed requires an asymptotic gain-frequency plot of the given open-loop transfer function. The plot is divided into three regions, viz., the high-gain region, the low-gain region, and the region near the crossover frequency. The closed-loop real poles are determined for high-gain and low-gain regions from known relationships of closed-loop and open-loop functions. From the knowledge derived therefrom, the complex-conjugate roots (along with real roots, if any) are determined for the crossover frequency region.