Frequency Domain Constraints Research Articles

Achievable dynamic responses of general damped mass-chain systems

The problem of achievable dynamic responses of general damped mass-chain systems with controllers installed between the first two masses are investigated in this paper. Achievable dynamic response of a system is the sets of functions that system transfer functions can achieve with all linear time-invariant (LTI) stabilizing controllers. The problem arises in the disturbance control of damped multi-degree-of-freedom (MDOF) vibration systems, such as vehicle suspension systems subject to road and load disturbances and multi-storey building systems subject to seismic and wind disturbances. The sets of functions that system transfer functions can achieve with stabilizing controllers and different system measurements are obtained by the Youla parametrization. By analysing achievable functions of system transfer functions, necessary and sufficient conditions (or complete sets of constraints) of system transfer functions are derived. It can be shown that compared with our previous work on achievable dynamic responses of an undamped mass-chain system, the necessary and sufficient conditions of transfer functions of a damped mass-chain system distribute only in the low-frequency range and the high-frequency range. This work generalizes the results of achievable dynamic responses of two-degree-of-freedom (2-DOF) vibration systems into MDOF vibration systems. The results obtained in this work present the boundaries of the transfer functions of damped MDOF vibration systems, and determine frequency-domain constraints of system transfer functions regardless what stabilizing controllers are used.

Accurate Spatial-Frequency Response Controllable Frequency Invariant Beampattern Synthesis With Minimum Beamwidth

This communication proposes a new relaxation variable based cost function for the problem of frequency invariant (FI) beampattern synthesis. Two constraints in the spatial and frequency domains are imposed on the optimization problem. The objective of sparsifying the relaxation variable is exploited in constructing the constraint in the spatial domain, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -spatial response variation (SRV) is introduced in the frequency domain constraint to reduce frequency variance. These constraints enable a desirable trade-off between beamwidth and FI properties while achieving accurate spatial-frequency response control. Since the resulting optimization problem is sparse and non-convex, it is then proposed to be solved by exploiting the reweighted- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm in this paper. The remarked feature of the new approach is the improved target detection and anti-interference performance in radar and communication systems without waveform distortion. Simulation results validate the effectiveness of the proposed method.

A Controller Design Method for Drag-Free Spacecraft Multiple Loops With Frequency Domain Constraints

Space-based gravitational wave detection requires a strict level of residual acceleration ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-15} \mathrm{~m/s}^{2} / \sqrt{\text{Hz}}$</tex-math></inline-formula> in the frequency band of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.1\text{mHz}\sim 1\text{Hz}$</tex-math></inline-formula> ) on the test masses along the sensitive axes. Because of the configuration of the detection spacecraft with two test masses, there are complex couplings between the spacecraft attitude, drag-free and suspension control loops in the drag-free and attitude control system. Moreover, the space environment disturbances and the limited noise levels of the actuators and sensors make it difficult for multiple control degrees of freedom to meet the index requirements at the same time. Currently, PID and <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> methods are mainly used for its controller design, where the system is decoupled and divided into relatively independent control loops, and the controllers are designed to meet the requirements separately. However, parameter tuning usually requires empirical trial and error, leading to the low design efficiency. And the coupling relationships between loops cannot be well described and treated mathematically. Therefore, a controller design method for drag-free spacecraft multi loops is proposed in this paper, where the index requirements are transformed into frequency domain constraints and the optimization objectives are designed for better performances according to the control characteristics of different loops. Then the controllers are tuned by multi-population genetic algorithm improving the design efficiency. As mentioned, under the premise that the index requirements are all met, the couplings between loops are considered and some of the performances of the system can be optimized, such as the residual acceleration acting on the test masses. Numerical simulation and comparison verify the effectiveness of this method.

H∞-Based Control Design for Grid-Forming Inverters With Enhanced Damping and Virtual Inertia

Grid-forming inverters (GFMIs) are identified as an important asset for achieving renewable energy-rich power grids. GFMIs are attracting significant attention due to their superior characteristics over grid-following inverters in both grid-connected (GC) and standalone (SA) scenarios. In this article, a second-order discrete-time controller is proposed to achieve a well-damped step response for power reference commands and improved virtual inertia provision capability. In this article, a control design method based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty} $ </tex-math></inline-formula> is proposed, which is based on the frequency response of the system, to tune the proposed controller. The proposed control design presents a methodical process to specify the desired performance indices through frequency-domain constraints. The performance of the controller is thoroughly validated analytically and through simulation results. The superior performance of the proposed controller over the virtual synchronous generator controller in terms of tracking performance and virtual inertia provision capability is verified through experimental results.

Design of discrete-time matrix all-pass filters using subspace Nevanlinna pick interpolation

Unitary matrix-valued functions of frequency are matrix all-pass systems, since they preserve the norm of the input vector signals. Typically, such systems are represented and analyzed using their unitary-matrix valued frequency domain characteristics, although obtaining rational realizations for matrix all-pass systems enables compact representations and efficient implementations. However, an approach to obtain matrix all-pass filters that satisfy phase constraints at certain frequencies was hitherto unknown. In this paper, we present an interpolation strategy to obtain a rational matrix-valued transfer function from frequency domain constraints for discrete-time matrix all-pass systems. Using an extension of the Subspace Nevanlinna Pick Interpolation Problem (SNIP), we design a construction for discrete-time matrix all-pass systems that satisfy the desired phase characteristics. An innovation that enables this is the extension of the SNIP to the boundary case to obtain efficient time-domain implementations of matrix all-pass filters as matrix linear constant coefficient difference equations, facilitated by a rational (realizable) matrix transfer function. We also show that the derivative of matrix phase constraints, related to the group delay at the interpolating points, can be optimized to control the all-pass transfer matrices at the unspecified frequencies. Simulations show that the proposed technique for unitary matrix filter design performs as well as traditional DFT based interpolation approaches, including Geodesic interpolation and the popular Givens rotation based matrix parameterization.

Bayesian Sparse Blind Deconvolution Using MCMC Methods Based on Normal-Inverse-Gamma Prior

Bayesian estimation methods for sparse blind deconvolution problems conventionally employ Bernoulli-Gaussian (BG) prior for modeling sparse sequences and utilize Markov Chain Monte Carlo (MCMC) methods for the estimation of unknowns. However, the discrete nature of the BG model creates computational bottlenecks, preventing efficient exploration of the probability space even with the recently proposed enhanced sampler schemes. To address this issue, we propose an alternative MCMC method by modeling the sparse sequences using the Normal-Inverse-Gamma (NIG) prior. We derive effective Gibbs samplers for this prior and illustrate that the computational burden associated with the BG model can be eliminated by transferring the problem into a completely continuous-valued framework. In addition to sparsity, we also incorporate time and frequency domain constraints on the convolving sequences. We demonstrate the effectiveness of the proposed methods via extensive simulations and characterize computational gains relative to the existing methods that utilize BG modeling.

Frequency Separation Control for Drag-Free Satellite With Frequency-Domain Constraints

For a drag-free satellite, one core technology required to achieve the mission requirements is drag-free control. The purpose of control is to offset the interference such as sunlight pressure, gravitational gradients of Earth and Moon, nonspherical perturbation, etc. Currently, the drag-free controller design is mainly aimed at the full frequency band. This will inevitably mix the control signal into the scientific measurement signal, thereby interfering with the processing of scientific data. Besides, the control at the full frequency band will increase fuel consumption. To solve the above problems, this article presented the controller design method for a drag-free satellite with scientific measurement constraints, which covers motion model establishing, coordinate axis decomposition, frequency separation control strategy formulation, H∞ mixed sensitivity controller design, controller stability analysis, and performance results.

Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part

Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This paper presents an identification workflow of a multi-resonant mechanical part in direct drive with up to three high-frequency mechanical resonances. In many methods, the identification of a discrete time (DT) model is applied, and its results are transformed into a continuous-time (CT) representation. The transformation from a DT model to a CT model has limitations due to nonlinear mapping of discrete to continuous frequencies. This problem may be overcome by identification of CT models in the frequency domain. This requires usage of a discrete Fourier transform to obtain frequency response data as complex numbers. The main work presented in this paper is the appropriate fitting of a CT model of a direct-drive mechanical part to complex number datasets. Fitting to frequency response data is problematic due to the attraction of unexcited high frequency ranges, which lead to wrong identification results of multi-mass (high order) drive systems. Firstly, a CT fitting problem is a nonlinear optimization problem, and, secondly, complex numbers may be presented in several representations, which leads to changes in the formulation of the optimization problem. In this paper, several complex number representations are discussed, and their influence on the optimization process by simulation evaluation is presented. One of the best representations is then evaluated using a laboratory setup of direct drive with unknown parameters of three high mechanical resonance frequencies. The mechanical part of the examined direct drive is described by three mechanical resonances and antiresonances, which are characteristic of a four-mass drive system. The main finding is the addition of frequency boundaries in the identification procedure, which are the same as those in the frequency range of the excitation signal. Neither a linear least-square algorithm nor a nonlinear least-square algorithm is suitable for this approach. The usage of nonlinear least-square algorithm with constraints as a fitting algorithm allows one to solve the issue of modeling multi-mass direct-drive systems in the frequency domain. The second finding of this paper is a comparison of different cost functions evaluated to choose the best complex number representation for the identification of multi-mass direct-drive systems.

Robust fuzzy delayed sampled-data control for nonlinear active suspension systems with varying vehicle load and frequency-domain constraint

This article studies the Takagi-Sugeno (T-S) fuzzy delayed sampled-data mathcal {H}_infty control problem for a class of intelligent suspension systems with varying vehicle load and frequency-domain constraint. The T-S fuzzy model is utilized to characterize the varying vehicle load. Considering the transmission delay, a robust fuzzy delayed sampled-data control mechanism is newly propounded for suspension systems. According to the Lyapunov stability theory, a useful theorem is proposed based on the Wirtinger inequality to guarantee the states of the active suspension system being asymptotically stabilized with the required mathcal {H}_infty performance by the proposed controller. Moreover, the suspension constrained requirements are also satisfied within the finite frequency domain. Finally, simulation examples are presented to attest to the usefulness and superiority of the proposed controller.

Comb-partitioned frequency-domain constraint adaptive algorithm for active noise control

Active noise control (ANC) is gaining credence as an effective approach in mitigating low-frequency urban noise. Current ANC algorithms that attenuate noise across the full audio frequency band, often exert control effort excessively at higher frequencies. Moreover, such unrestrained control unavoidably attenuates some critical sounds, such as alarms and warning signals. In practice, excessive control effort in ANC usually results in output-saturation distortion, which affects the adaptive system stability and degrades the residual audio quality. To provide greater flexibility of control in frequency bands of interest without incurring output saturation, this paper proposes two variants of the filtered reference comb-partitioned frequency-domain adaptive filter (FxCFDAF) algorithm, namely the leaky FxCFDAF and drop-out FxCFDAF algorithms, which exert output-effort constraint at the control filter in the frequency domain. In addition, the comb-partitioning approach in the proposed FxCFDAF algorithms is delayless and computationally-efficient, which are essential for practical implementation, unlike the conventional frequency-domain adaptive algorithm. Experimental simulations carried out on measured primary and secondary paths validate the proposed algorithms’ advantage over the conventional FxLMS algorithm in mitigating large-amplitude noise without output saturation.

Data-driven robust controller design by geometric constraints in frequency-domain

This paper aims to propose an improved method for designing the robust controller that satisfies the mixed sensitivity criterion. In robust controller design using frequency-domain data, the important task is to find the appropriate constraints for the design parameters. In our method, the controller is designed with fixed-order linearly parameterized structure and the desired robust performance criteria are represented by the geometrical constraints for open-loop frequency characteristic. Then the constraints lead to the convex searching problem for the parameters of controller so that we obtain the optimal parameters by the numerical iterative algorithm for the finite number of the linear inequalities. The significance of our research is that the proposed method is more reliable for the robust performance criterion because it does not require the approximation for the constraint. The control simulation for the robust PID controller shows the improved transient response.

Multi-Objective Digital PID Controller Design in Parameter Space and its Application to Automated Path Following

This paper presents a multi-objective digital PID controller design method using the parameter space approach of robust control. Absolute stability is treated first by finding the digital PID controller gain parameter space corresponding to closed loop poles being inside the unit circle. Additionally, phase margin, gain margin and a mixed sensitivity bound are treated as frequency domain constraints. Determination of digital PID controller parameter space regions satisfying these constraints is presented. All of these regions are superimposed to obtain a multi-objective digital PID controller gain parameter space solution region. The path following controller design of an automated driving vehicle is used as an example to illustrate the method. This multi-objective parameter space design approach can be extended to other digital controller forms also.

Room Impulse Response Reshaping and Crosstalk Cancellation Using Convex Optimization

In this article, a new convex formulation for the acoustic channel-equalization problem is proposed and efficient ways for solving it are presented. Both the alternating direction method of multipliers and a proximal algorithm are studied for optimization. Time-domain and frequency-domain constraints are included in an equal way, allowing for simultaneous reverberation reduction and frequency-response equalization. Rather than aiming at full channel equalization, we follow the channel-reshaping paradigm proposed in earlier works and try to push the reverberation tail under the temporal masking limit of the human auditory system, thus making reverberation inaudible for human listeners. While the algorithm is presented for the multiple-input-multiple-output (MIMO) scenario, the single-channel case is included as a special case. Comparisons with methods from the literature for the single- and multi-channel cases show that the new algorithm has faster convergence than the known ones. The proximal algorithm even allows for solving extremely large problems with very low memory demand.

Data-Driven Distributed Combined Primary and Secondary Control in Microgrids

This brief paper presents a comprehensive data-driven distributed combined primary/secondary controller design method for microgrids. This method provides transient and steady-state performances, including power sharing and voltage and frequency restoration while guaranteeing stability for fixed communication delays. Measured data are directly used for controller design, and no knowledge of the model structure or the physical parameters of the grid is required. Moreover, no assumption is made on the X/R ratio of the feeders. All control specifications are formulated as frequency-domain constraints on the two-norm of weighted sensitivity functions. Then, using a recently developed frequency-domain robust control design method, a distributed fixed-structure controller is synthesized in one step. The performance of the obtained controller is validated using hardware-in-the-loop (HIL) experiments. The results show considerable improvement in transient performance while providing power sharing and voltage and frequency restoration with a distributed implementation.

Ciphertext-only attack on optical scanning cryptography

The optical scanning cryptography (OSC) is one of the most utilized optical encryption systems. Our research is inspired from the observation that there is a linear system property within the ciphertext expression equation of OSC. Given the linear system property, it is feasible to recover the plaintext with cipher-only attack (COA). Our proposed COA method converts the problem of COA into a phase retrieval problem with a single intensity measurement. With the frequency domain constraint and the object domain support obtained from the ciphertext of OSC, the hybrid input-output (HIO) algorithm can be used to recover plaintext. Simulation results demonstrate the feasibility and robustness of the attack. This shows for the first time that the OSC scheme is vulnerable to COA attack.

Convex Optimization-Based Control Design for Parallel Grid-Connected Inverters

This paper presents a novel frequency-domain approach toward the control design for parallel grid-connected voltage source inverters (VSIs) with LCL output filters. The proposed method allows the controllers of multiple VSIs to be designed in a single step, and inherently attenuates the resonances introduced by the output filters and coupling effects while guaranteeing stability. Performance specifications such as desired closed-loop bandwidth, decoupling or robustness toward multi-model uncertainty can be specified through frequency-domain constraints. Furthermore, controllers can be designed in a plug-and-play fashion. The designed controllers are equivalent in structure to multi-variable PI controllers with filters. As the control design is based on the frequency response of the system, the algorithm is independent of the model order, which allows the use of large and high-order models. The performance of the method is demonstrated on a relevant example of a low-voltage distribution grid with five VSIs, and the results are validated both in numerical simulation using MATLAB/Simulink as well as in power-hardware-in-the-loop experiments.

Epsilon-multiobjective particle swarm optimization-based tuning of sensitivity functions for polynomial control design

In this paper, a novel systematic method for the polynomial controllers (denoted as RST controllers) design and tuning is proposed and successfully implemented based on an epsilon-multiobjective particle swarm optimization (ε-MOPSO) algorithm. The ε-domination concept is used to further improve both properties of the non-premature convergence towards Pareto-optimal sets and the diversity among the found solutions. The RST polynomials coefficients’ computation is formulated as a constrained multiobjective optimization problem under operational frequency-domain constraints. The proposed methodology aims to optimize a desired output sensitivity function satisfying nominal performance and H∞ robustness specifications of the closed-loop system. The use of a suitable fixed parts of the optimized output sensitivity function will provide partial poles placement of the closed-loop dynamics. The inverse of such an optimized desired sensitivity function defines the performance and robustness H∞ weighting filter. Such a proposed ε-MOPSO algorithm is firstly compared with several homologous MOPSO, non-dominated sorting genetic algorithm II (NSGA-II) and multiobjective differential evolution (MODE) algorithms for a benchmark of multiobjective test functions. The algorithms’ performances are evaluated in terms of several metrics in order to show the superiority and the effectiveness of the proposed method. An application to the axis position control of a flexible transmission system with varying loads is then performed. Demonstrative simulations are carried out to show the remarkable superiority and effectiveness of the proposed ε-MOPSO-tuned digital RST controllers compared with several well-known methods available in the literature.

Structural vibration attenuation using a fractional order PD controller designed for a fractional order process

Structural vibration is a highly studied topic, especially in civil structures. Unwanted earth vibrations during seismic activity endanger life and often destroy buildings. In this paper, a Fractional Order Proportional Derivative controller is designed with the purpose of vibration mitigation in a three-story building. The experimental setup consists of a third floor building equipped with an active pendulum attached to the last floor. The controller is designed for the fractional order mathematical approximation of the structure by imposing frequency domain constraints such as gain crossover frequency, phase margin and robustness to gain variations. The validity of the controller is analyzed considering the simulated behavior of the compensated building to the El Centro earthquake and experimental disturbance rejection performance.

Broadband Adaptive Beamforming of Conformal Arrays for Wireless Communications Based on Generalized Sidelobe Canceller

Conformal arrays are increasingly used in recent wireless communication systems due to their flexibility in mounting on arbitrary surfaces. Many of such systems require working with broadband signals. However, designing conformal arrays has been limited mostly to pattern synthesis techniques due to the complexity imposed by the different contribution of individual antenna patterns to the overall array response. Such pattern synthesis techniques greatly confine the application of the beamformer in dynamic environments since they are fundamentally non-adaptive data independent methods. In this article, the conventional space–time broadband generalized sidelobe canceller (GSC) is used to develop an adaptive method for an arbitrarily-shaped conformal array. The constraint matrix assumed for the main beam of the conventional GSC structure is modified to incorporate the pattern of each individual element. This treatment allows the element responses to be directly involved in the weight adjustment algorithm and contribute to the array overall response without having any additional complexity. The proposed method can handle different types of the constraints, although the analysis presented here is based on the angle–frequency domain constraints which nevertheless eliminates the presence of the pre-steering delays and ensures a frequency invariant beampatterm required for wideband beamforming. The simulation results which are presented for a typical cylindrical array show that the proposed method can create the desired broadband beampattern with high performance and in an adaptive manner.

Design and Analysis of a Conductance Compensator for Keeping Constant Bandwidth and Output Impedance in Average Current Mode Control

Take the case of parallel modules in battery discharging regulator of power conditioning unit, which is based on Weinberg topology, a conductance compensator used in average current mode control is proposed in this paper, which could ensure constant loop bandwidth and output impedance when the number of operating parallel modules changes. The design principle of conductance compensator is shown as that the total conductance coefficient keeps constant when the number of operating parallel modules changes. Besides, a circuit of the conductance compensator, and the timing between the regulation of conductance compensator and ON/OFF of parallel modules, as well as the frequency-domain constraints of each function part in outer voltage control loop, are also illustrated. Additionally, measurements of the loop characteristic and output impedance of regulated power bus with different numbers of operating parallel modules, as well as the voltage ripple and current waveforms at the ON/OFF moment of parallel modules (four parallel modules in total), have been carried out, validating the design purpose of the proposed conductance compensator.