Closed-loop Transfer Function Research Articles

A study into the fluid power control characteristics of a hydrostatic transmission for mobile machinery

In response to improve the quality and level of hydrostatic transmission (HST) products for modern mobile machineries, the closed-loop transfer functions of a HST are established by mathematical modeling, a comprehensive testing equipment is developed employing a proportional relief valve for automatic program loading and fuzzy-PID oil temperature control, the testing equipment is capable of conducting various performance tests for various models of HST integrated pump-motor products, including factory and type tests, especially continuous impact and endurance performance tests under high temperature and high-speed conditions. Comprehensive performance test of the above test sample is carried out using the developed equipment, that the test results agree well with the previous simulation results verifies the correctness of the established theoretical analysis model. The obtained theory and equipment from this work provide theoretical and experimental technical support for improving design and development of high-end fluid components for modern mobile machinery HST.

Small-Signal Stability Analysis and Voltage Control Parameter Design for DC Microgrids

Small-signal instability issues will occur in the DC microgrid when the high-frequency oscillation peaks of the voltage closed-loop transfer function are not effectively suppressed. To ensure the small-signal stability of DC microgrids, the concept of a small-signal stability domain for voltage control parameters is proposed. Based on the voltage closed-loop transfer function, a small-signal-stability-domain-solving algorithm is proposed. With this stability domain, the impact of voltage-proportional coefficient and voltage-integral coefficient on oscillation frequency (or damping factor) is quantitatively analyzed. In addition, the influence of current control parameters on the small-signal stability boundary is also analyzed. With the introduction of this stability domain, a design method for voltage control parameters has been proposed. The voltage control parameters, which are quantitatively designed by this method, are able to maintain the small-signal stability of the system. Finally, based on the RT-BOX hardware-in-the-loop experimental platform, a switching model for a typical DC microgrid is established. Additionally, the effectiveness of the proposed algorithm and designed control parameters is verified by multiple sets of experimental results.

Analysis of a Simplified Predictive Function Control Formulation Using First Order Transfer Function for Adaptive Cruise Control

This paper presents a formulation and analysis of a low computation Predictive Functional Control (PFC), which is a simplified version of the more advanced Model Predictive Control (MPC) for an Adaptive Cruise Control (ACC) system by using a representation of first order closed-loop transfer function. In this work, a non-linear mathematical model of vehicle longitudinal dynamics is considered as a control plant. Then, a simple Proportional Integral (PI) controller is employed as an inner loop to identify the first-order relationship between its actual and desired trajectory speed according to the reasonable time constant based on the logical response of pedals pressing. To directly control the whole plant, the PFC is formulated as an outer loop to track the desired speed together with the convergence rate based on a user preference while satisfying constraints related to acceleration and safe distancing. Since PFC is formulated based on the first-order transfer function, the prediction and tuning processes are straightforward and specific to this system. The simulation results confirm that the proposed controller managed to track the desired speed while maintaining a comfortable driving response. Besides, the controller also can retain safe distancing during the car following application, even in the presence of unmeasured disturbance. In summary, this framework can avoid the need to formulate an inverse non-linear model that is typically used when deploying a hierarchical control structure to compute the throttle and brake pedals pressing as it has been replaced with an inner loop PI controller. The performance also is comparable yet more conservative due to the simplification. These findings can become a good reference for designing and improving the ACC controller, as the framework can be easily generalized for any type of vehicle for future work.

Control analysis of an underactuated bio-inspired robot

Abstract This article is devoted to the control of bio-inspired robots that are underactuated. These robots are composed of tensegrity joints remotely actuated with cables, which mimic the musculoskeletal system of the bird neck. A computed torque control (CTC) is applied to these robots as well as an original control called pseudo computed torque control (PCTC). This new control uses the dynamics and the pseudo-inverse of the Jacobian matrix. The stability of the two proposed controls is then analyzed through linearization of the dynamic model and expression of the closed-loop transfer function in the Laplace domain. We show that, depending on the desired trajectory, the CTC can be unstable when the controlled variables are the end effector position and orientation. For a robot with many joints and a limited number of cables, the CTC is always unstable. Instead, the PCTC shows a large domain of stability. The analysis is complemented by experimental tests demonstrating that the CTC and PCTC exhibit similar performance when the CTC is stable. Furthermore, the PCTC maintains stability on trajectories where the CTC becomes unstable, showing robustness to perturbations as well.

Research on control parameter optimization of LCC-HVDC system based on zero-pole optimal position distribution

The proportional-integral (PI) control is widely adopted as the leading controllers of the line-commutated converter high-voltage direct current transmission system (LCC-HVDC), while unreasonable coefficients setting will result in the DC system instability and aggravate system dynamic performance. In order to improve the overall response performance of the system, a tuning method of the controller parameters guided by the linearized zero-pole transfer function of the DC system is proposed. Firstly, the small signal analysis method is used to formulate the closed-loop transfer function model at the stable operating point. According to the position of zero and pole, the objective function which can quantitatively reflect the dynamic and steady state characteristics of the DC system is derived. Furthermore, combined with the particle swarm optimization (PSO) intelligent optimization algorithm, the multi-group control parameters of the system are optimized. Finally, by comparing the time domain numerical simulation results before and after parameter optimization, it is verified that the proposed tuning method can effectively improve the dynamic and steady-state characteristics of the DC system.

Closed-loop identification of stabilized models using dual input–output parameterization

This paper introduces a dual input–output parameterization (dual IOP) for the identification of linear time-invariant systems from closed-loop data. It draws inspiration from the recent input–output parameterization developed to synthesize a stabilizing controller. The controller is parameterized in terms of closed-loop transfer functions, from the external disturbances to the input and output of the system, constrained to lie in a given subspace. Analogously, the dual IOP method parameterizes the unknown plant with analogous closed-loop transfer functions, also referred to as dual parameters. In this case, these closed-loop transfer functions are constrained to lie in an affine subspace guaranteeing that the identified plant is stabilized by the known controller. Compared with existing closed-loop identification techniques guaranteeing closed-loop stability, such as the dual Youla parameterization, the dual IOP requires neither a doubly-coprime factorization of the controller nor a nominal plant that is stabilized by the controller. The dual IOP does not depend on the order and the state-space realization of the controller either, as in the dual system-level parameterization. Simulation shows that the dual IOP outperforms the existing benchmark methods.

A feedforward control for increasing the damping effect of enhanced current-controlled virtual synchronous generator

Novel grid-forming control strategies based on the virtual synchronous generator (VSG) algorithm are becoming a key technology for power converters in modern hybrid power systems. This paper considers an alternative current-controlled VSG structure (CC-VSG). However, this structure is complex third-order system and is characterized by the lack of damping torque when the grid strength changes. Therefore, in this paper an enhancement of the CC-VSG damping properties via a feedforward controller is proposed. The analysis of the closed-loop transfer function demonstrates the reduction of the model order to the second order due to the proposed controller. By analyzing the state-space model, the predominant impact of the gain of the developed controller on the low-frequency roots is proved. As a result, it is concluded that the enhanced CC-VSG structure is efficient, stable and can be flexibly tuned to obtain any desired dynamic response under different grid strength conditions and load variation.

A comparative study on PI-PD controller design using stability region centroid methods for unstable, integrating and resonant systems with time delay

In this paper, controller tuning methods based on stability region centroid methods reported in the literature are used to design PI-PD controllers for unstable, integrating and resonant systems with time delay. By analyzing the stability boundary locus (SBL) for the PD controller, which is utilized in the inner loop of this structure, the controller parameters are obtained using three methods which are the Weighted Geometric Center (WGC), Centroid of Convex Stability Region (CCSR), and Stability Triangle Approach (STA). These techniques were applied analytically, step by step. For the closed loop transfer function obtained in the inner loop of the controlled system, these three methods were utilized to design the PI controller in the outer loop, individually. Unit step responses of the controlled system, using PI-PD gains determined by each method, have been obtained. Furthermore, a disturbance of a certain time and amplitude was added to the systems to test the disturbance rejection behavior and the robustness performance of the methods. Perturbed responses were obtained through changing the model parameters at a certain rate. Time domain performance metrics were analyzed to compare the responses. The simulations were evaluated using settling time, rise time, and percentage overshoot as the assessment criteria. As a result of this study, the effectiveness of three methods, namely WGC, CCSR, and STA, in controller design for unstable, integrating, and resonant time-delay systems has been demonstrated. In addition, a comparison of time domain performance metrics is presented for the nominal and perturbed systems. Based on these comparisons, it is concluded that the methods outperform each other only in some time response performance measures. The presented results showed the advantages of these methods over each other in terms of some performance criteria. The contribution of this study to the literature is the comparative analysis of these three analytical methods.

Parametric Sensitivity Analysis of Stability Margins of Holos-Quad Microreactor

An analysis of the stability margins of the innovative Holos-Quad microreactor design is presented. This high-temeprature gas-cooled reactor (HTGR) system is designed to operate fully autonomously with passive safety mechanisms. Therefore, the inherent stability of the reactor is of great importance. Using a point-reactor model, which couples point kinetics to thermal-hydraulic heat balance equations and includes reactivity feedback effects of the fuel and moderator temperatures, the closed-loop transfer function of the reactor is derived. Applying the approach of linear systems and control theory, both the gain and phase margins of the Holos-Quad design are obtained. The analysis demonstrates that the design is stable, with an infinite gain margin and a finite phase margin. A parametric uncertainty quantification study is also performed using a total Monte Carlo approach. The stability of the reactor for different power levels, such as during reactor startup or load-following transients, is also explored. Finally, two sensitivity analysis methods are applied, namely, multiple regression (deriving standardized regression coefficients) and variance-based sensitivity analysis (known as the Sobol method), to study the contribution of each of the parameters to the stability margins’ uncertainty. This analysis improves our understanding of the role of each of the parameters in the stability of the reactor.

Current coordinated distribution and voltage optimization control for multi-VSGs system considering nonlinear and negative sequence loads

In a microgrid system where multiple virtual synchronous generators (VSGs) are interconnected through high impedance cables, the total output negative sequence and harmonic current of multiple VSGs cannot be coordinated based on the capacity of each power conversion system (PCS). In addition, there is significant distortion in the voltage at the point of common coupling (PCC). Because the impedance amplitude and impedance angle of the cable change with the harmonic frequency, the resistive virtual impedance reshaping method and fixed impedance angle virtual impedance reshaping method used in the current research cannot solve the harmonic current distribution problem. To solve the above problems, a multi-frequency points VSG impedance reshaping control strategy is proposed in this paper, which can adjust the resistive and inductive output impedance of each harmonic frequency independently. The strategy is based on the harmonic separation algorithm of LPF with Feedforward Compensation (FCLPF) and the voltage controller of Vector Proportional Integral (VPI) in fundamental dq rotation coordinate system, which effectively improve the flexibility and accuracy of harmonic impedance reshaping. Among them, FCLPF harmonic separation algorithm has the characteristics of target frequency bandpass and non-target frequency notch, and can eliminate the coupling interference of each harmonic virtual impedance when accumulating virtual impedance voltage references at various frequency points. The closed-loop transfer function of the multi-parallel VPI voltage controller has the characteristics of unit gain and zero phase shift at each harmonic frequency point, which means the static response error of virtual impedance voltage command can be almost completely eliminated. Under the proposed control strategy, the fundamental positive power can be allocated according to the droop coefficient, the fundamental negative current and harmonic current can be allocated according to the sum of the reshaped virtual impedance and the actual line impedance. Reshaping virtual impedance at each harmonic frequency to negative value can also compensate the harmonic voltage drop on the high impedance cable and improve the voltage quality at the PCC.

Time-domain instability mechanism for artificial boundary condition of semi-infinite medium described by discrete rational approximation

The use of discrete rational approximation functions to represent foundation dynamic impedance plays a crucial role in the time-domain analysis of soil-structure interaction regarding artificial boundary. In modeling, the rational approximation functions need to be transformed into time-domain recursive models for incorporation into time-history analysis. However, this method also suffers from uncertainties in parameter identification and instability in time-domain analysis when the time-domain recursive models of soil are coupled with upper structure. The stability issue in artificial boundary coupled time-domain computation has not been effectively addressed. This paper establishes the closed-loop transfer function of the coupled system and analyzes the causes of instability in the coupled system based on gain margin analysis. Different numerical simulations demonstrate that the major cause of artificial boundary system instability is the description errors of discrete rational approximation functions beyond the fitting frequency range.

Current sensorless model predictive control for LC-filtered voltage source inverters based on sliding mode observer

Abstract In recent years, model predictive control (MPC) has gained significant traction within the realm of LC-filtered voltage source inverters (VSIs). In order to reduce the number of current sensors in conventional MPC, this paper proposes a MPC scheme without current sensors for LC-filtered VSIs. Firstly, this paper analyzes the mathematical model of LC-filtered VSIs and specifies the predictive control strategy based on capacitive current. On the basis of considering only the fundamental wave components of the capacitance current, this paper establishes a new sliding mode observer to observe the capacitance current. In order to ensure the stability of the system, the stability of the proposed sliding mode observer is analyzed using Lyapunov stability criterion, and the influence of the sliding mode gain on the current and voltage observations is also analyzed according to the closed-loop transfer function, giving the design method of the sliding mode gain. In addition, the parameter sensitivities of the newly proposed method and the conventional method are analyzed in detail in this paper. The results show that the method proposed in this paper does not depend on the filter inductance and the observed capacitance current have smaller errors and stronger parameter robustness than the conventional method. The comparative experimental study verifies the feasibility of the control scheme proposed in this paper.

Improvement of the linear quadratic regulator control applied to a DC-DC boost converter driving a permanent magnet direct current motor

This article discusses a new robust control technique that enables the DC-DC boost converter driving a permanent magnet direct current (PMDC) motor to operate in high static and dynamic performances. The new technique is based on the design of a both linear quadratic regulator (LQR) and linear quadratic regulator-proportional integral (LQR-PI) type controllers, which have the advantage of eliminating oscillations, overshoots and fluctuations on different characteristics in steady-state system operation. In order to increase the output voltage, the LQR regulator is combined with a first-order system represented in the form of a closed-loop transfer function, the latter raising the output voltage to 24 volts, this voltage is enough to drive the permanent magnet direct current motor. The contribution of this paper is the creation of a robust control system represented in the form of a hybrid corrector able to regulate steady-state and transient disturbances and oscillations as well as to increase DC-DC boost converter output voltage for the PMDC motor to operate at rated voltage. The results of the three control techniques are validated by MATLAB Simulink.

Low order speed harmonic suppression in FOC-PMSM based on the closed-loop transfer mechanism of injected voltage

In the field oriented control (FOC) permanent magnet synchronous motor (PMSM) servo system, torque ripple impairs motor performance. Harmonic injection methods can suppress torque ripple by injecting additional voltage harmonic to offset the existing speed harmonic. However, since FOC is a closed-loop motion control strategy, the transfer path from injected voltage harmonic to speed harmonic is affected by FOC, especially in very low frequency. Due to the influence of FOC on the transfer function, the relation between the injected voltage harmonic and speed harmonic varies with operating conditions and motor control parameters. It causes the existing harmonic injection methods ineffective to suppress low order speed harmonics. To solve the problem, in this paper, the closed-loop transfer mechanism of injected voltage harmonics is analyzed and the closed-loop transfer function is derived. Based on the derived closed-loop transfer function, a low order speed harmonic suppression method is proposed. With the derived transfer function, the proposed method can adapt to the variations of the relation between low order injected voltage harmonic and speed harmonic under different operation conditions. Finally, the accuracy of the derived closed-loop transfer function and the effectiveness of the proposed low order speed harmonic suppression method are evaluated by experiment.

Research on the Current Control Strategy of a Brushless DC Motor Utilizing Infinite Mixed Sensitivity Norm

During the brushless DC (BLDC) motor working process, the system encounters inevitable uncertainties. These ambiguities stem from potential fluctuations, random occurrences, measurement inaccuracies, varying operational conditions, environmental shifts such as temperature alterations, among other factors. Uncertainties, an inherent aspect of any real control system, can be broadly classified into two categories: sensor signal uncertainties and discrepancies between the mathematical and actual models due to parameter perturbations. To mitigate the impact of sensor noise and parameter perturbations on the BLDC motor, a robust control strategy utilizing infinite norm mixed sensitivity based on PI control strategy (PI-H∞-MIX) is proposed in this paper. Firstly, the closed-loop control structure and transfer function model of the BLDC motor control system current loop are analyzed based on the current loop circuit topology, and then, the model parameters perturbation is analyzed, and the multiplicative uncertainty bound is given. In addition, the appropriate weighting function is selected to ensure the robustness of the system. In this case, the controller design problem is transformed into the H∞ standard control problem, and then, the system augmentation matrix is established, and the controller is solved by Matlab/Simulink. Finally, the performances of the traditional PI control strategy and the PI-H∞-MIX are compared and analyzed. The results show that (1) the proposed PI-H∞-MIX strategy can improve the control system robustness under the parameter perturbation condition effectively, and (2) the proposed PI-H∞-MIX strategy can suppress the noise signal of the sensor.

One-Step Ahead Control Using Online Interpolated Transfer Function for Supplementary Control of Air-Fuel Ratio in Thermal Power Plants

Recently, the environmental problem has become a global issue. The air to fuel ratio (AFR) in the combustion of thermal power plants directly influences pollutants and thermal efficiency. A research result was published showing that the AFR control performance of thermal power plants can be improved through supplementary control using dynamic matrix control (DMC). However, online optimization of DMC needs an extra computer server in implementation. This paper proposes a practical AFR control with one-step ahead control which does not use online optimization and can be implemented directly in existing distributed control system (DCS) of thermal power plants. Closed-loop transfer function models at three operating points are independently developed offline. Then, an online transfer function using interpolation of offline models is applied at each sampling step. A simple one-step ahead control with online transfer function is applied as a supplementary control of AFR. Simulations with two different type power plants, a 600 MW oil-fired drum-type power plant and a 1000 MW ultra supercritical (USC) coal-fired once-through type power plant, are performed to show the effectiveness of the proposed control structure. Simulation results show that the proposed supplementary control can effectively improve the conventional AFR control performance of power plants.

Design and analysis of root locus based controllers

The root locus method is the classical method for analyzing the variation of the position of the poles of a closed-loop control system transfer function in the complex plane. It is also the basis for guiding the design of various controllers. Starting from the nature of the root locus, this paper takes a standard form of closed-loop feedback control system as an example, and analyzes in detail the internal logic of designing a controller and compensator by the root locus method. At the same time, software such as MATLAB/Simulink, and Octave are used. The working principles and properties of the PD controller; the lead and lag compensator, their interconnections, advantages, and characteristics, as well as the adjustment of parameters to better suit practical needs, are sorted out. The PD controller improves the system response, the lead compensator eliminates the PD controller’s defects, and the lag compensator reduces the steady-state error of the system. It provides help for understanding the essence of controller design and provides design ideas for control problems in actual engineering.

Implementation of Bio-inspired Algorithms in Designing Optimized PID controller for Cuk Converter for Enhanced Performance: A Software based Approach

This paper represents the idea of implementing bio-inspired algorithms in designing an optimized PID controller to investigate the stability and improve the performance of the closed-loop CUK converter. Bio-inspired algorithms (BIA) such as Firefly Algorithm (FA), Particle Swarm Optimization (PSO) and, Artificial Bee Colony (ABC) are stochastic optimization techniques and have been increasingly applied to attain optimal solution for designing and optimizing power converters in current times. The closed-loop transfer function of the CUK converter has been developed by the State Space Average (SSA) technique. This paper assesses both the cases of converter stability when it is integrated with the conventional PID controller and the BIA-PID controllers (FA-PID, PSO-PID, ABC-PID) and eventually compares the outcomes from all the controllers. For examining the stability of the system, three objective functions (IAE, ITAE, and ISE) and various performance specifications such as percentage of overshoot, rise time, settling time, and peak amplitude are tabulated. MATLAB and Simulink are used to carry out the simulations meticulously. Hence, a comparative analysis is illustrated in this paper to state a clear-sighted evaluation of the performances.

Comment on “Optimal tuning of sigmoid PID controller using nonlinear sine cosine algorithm for the automatic voltage regulator system”

In this short note, the relative stability results (based on root locus and Bode analyses) reported in “Optimal tuning of sigmoid PID controller using nonlinear sine cosine algorithm for the automatic voltage regulator system” (Suid and Ahmad, 2022) are analyzed. It is shown that the use of closed-loop transfer functions (CLTFs) should be avoided in relative stability analysis since they may lead to less accurate stability results. The present study affirms that the results of relative stability analysis obtained using loop transfer functions (LTFs) are more reliable and accurate.

Implementation Methods of Controllers Designed by $H_\infty$ Loop Shaping

When the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> loop-shaping controller is implemented as a unity feedback system, its step responses are sometimes unsuitable for tracking control, typically, displaying large overshoots. In this paper, the implementation method is studied for tracking control with small overshoots. Three implementation methods that are described by a unity feedback system, a previous simple two-degrees-of-freedom(2DoF) system, and a new simple 2DoF system proposed in this paper are examined. For the closed-loop transfer function of each system, the unstable zeros are analyzed and an upper bound of the peak gains is presented. These results show that the two simple 2DoF systems have adequate properties for tracking control with small overshoots. The new 2DoF system has good features that the system is minimum phase if the plant is minimum phase, and that the resonance peak gain is one. Their tracking performances are compared in several numerical examples.