Closed-loop Frequency Response Research Articles

Small-Signal Modeling and Parameter Extraction Method for Photovoltaic Cell Integration in Indoor Visible Light Communication Systems

Photovoltaic (PV) cells are being adopted as a viable and cost-effective option for implementing receivers within Visible Light Communication (VLC) systems, primarily in indoor environments. Accurately estimating the generated current and voltage of the PV cell based on incident light is crucial when designing VLC systems.For this assessment, the 1D2R electrical equivalent model, which incorporates a diode and two resistors, is employed.In AC small signal analysis, the diode is substituted by its dynamic counterpart, which comprises a dynamic resistance in parallel with an equivalent capacitance. This study introduces an approach to measure and characterize the small-signal parameters of a PV cell operating at the maximum power point (MPP), open circuit (OC), and short circuit (SC) bias points. This is achieved through a closed-loop frequency response system, calibrated to encompass illuminance levels ranging from 50 to 500 lux.The procedure for estimating the AC response of the PV cell is outlined, and the outcomes are subsequently employed in an analytical parameter extraction methodology. Experimental results from a 20 x 40 mm PV cell reveal that MPP represents the least favorable bias point in terms of bandwidth, whereas the SC bias point exhibits the most favorable performance. This observation validates the hypothesis that the optimal bias point for energy harvesting in PV cells is the worst bias point for communication purposes.

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Magnetic levitation system (MLS) is a typical nonlinear system that controls the position of a steel ball with the magnetic force of the electromagnetic actuator. Since disturbances, due to various external forces and modeling errors, may cause excessive vibration or poor command following, disturbance suppression is necessary to improve the control performance of the MLS. This paper presents a control performance improvement approach of an MLS with a disturbance observer (DOB). First, a mathematical model of the MLS was introduced and validated with the measured frequency response. The MLS steel ball was levitated with a proportional–integral–derivative (PID) controller and a DOB was designed based on the physical model of the MLS. Both disturbance rejection and command tracking performances of the MLS with the DOB were investigated with several design parameters such as PID gains and Q filter. The disturbance rejection and command tracking performances were improved by 76.1% and 64.7%, respectively by using DOB. Finally, the disturbance rejection and command-following performances of the MLS with the DOB were verified experimentally. The effectiveness and limitations of DOB were explained with measured closed-loop frequency responses.

Bias of anticipated non-parametric closed-loop frequency response for controller gain re-tuning

In data-driven controller re-tuning, when requirements exist for the closed-loop frequency response, it is essential that the estimated closed-loop frequency response for a new controller parameter set, correctly reflects the respective true closed-loop. To quantify the difference between the true and estimated frequency response, this paper presents the bias of the non-parametric closed-loop frequency response estimate for the closed-loop system with updated controller parameters. It is calculated for the case where the estimate of the closed-loop frequency response of the system with an initial controller is used, to estimate the new closed-loop frequency response with an updated controller. Such estimates are useful in the process of gain re-tuning based on closed-loop experiments, where new controller parameters are calculated to satisfy requirements for the closed-loop frequency response. It is shown that the estimate appears similar in structure to the indirect non-parametric plant estimate, and hence the bias is reduced with an increasing excitation-to-noise-ratio for the closed-loop experiment. It is also seen that the bias tends to zero when the change in the controller parameters tends to zero or the feed-forward is increased sufficiently. Simulation results demonstrate the concept for a flight-test-based gain re-tuning of a pitch rate controller for an aircraft.

Closed-Loop Frequency Analysis of Reset Control Systems

This article introduces a closed-loop frequency analysis tool for reset control systems. To begin with sufficient conditions for the existence of the steady-state response for a closed-loop system with a reset element and driven by periodic references are provided. It is then shown that, under specific conditions, such a steady-state response for periodic inputs is periodic with the same period as the input. Furthermore, a framework to obtain the steady-state response and to define a notion of closed-loop frequency response, including high order harmonics, is presented. Finally, pseudosensitivities for reset control systems are defined. These simplify the analysis of this class of systems and allow a direct software implementation of the analysis tool. This methods gives deeper insight into the performance of the system than that achieved with the describing function method.

Multi-loop PID controllers design with reduced loop interactions based on a frequency-domain direct synthesis method

A novel direct synthesis (DS) method for simultaneous and non-iterative design of multi-loop PID controllers for stable multivariable processes is presented in this article. We deal with the specifications of the desired closed-loop dynamics, which is a critical design decision in the DS method, for designing multi-loop controllers. Control loop interactions in multi-loop control systems are usually undesirable but unavoidable due to inter-channel interactions of multivariable processes. The main feature of the method is that the multi-loop control design aims at reducing the interactions among loops. The proposed DS method specifies the design target in terms of the frequency response of the desired closed-loop transfer function (CLTF) and synthesizes the controllers in the frequency domain. We develop an approach to effectively specify the desired closed-loop frequency response to achieve improved control performance by minimizing the sum of the magnitude of the interactive parts in the desired CLTF matrix. With the desired closed-loop frequency response and a process model, the frequency response of an ideal multi-loop controller is synthesized and then approximated to a PID controller. We provide simulation studies of three industrial benchmark processes and a nonlinear quadruple tank system to illustrate the design result and performance of the proposed method and make comparisons with several existing methods. Our results prove the effectiveness of the frequency-domain DS method. The proposed multi-loop PID controllers achieve reduced loop interactions and provide satisfactory overall performance.

Frequency Response Data-Based LPV Controller Synthesis Applied to a Control Moment Gyroscope

Control of systems with operating condition-dependent dynamics, including control moment gyroscopes (CMGs), often requires operating condition-dependent controllers to achieve high control performance. The aim of this brief is to develop a frequency response data-driven linear parameter-varying (LPV) control design approach for single-input single-output (SISO) systems, which allows improved performance for a CMG. A stability theory using a closed-loop frequency response function (FRF) data is developed, which is subsequently used in a synthesis procedure that guarantees local stability and performance. Experimental results on a CMG demonstrate the performance improvements.

Modeling and Performance of a Buck Converter Based on ‘Fuzzy Logic Soft Computing Technique’ for Low Voltage Operations

This present paper details a ‘fuzzy logic soft computing technique’ of designing a controller for a buck converter operating at low voltages. The dc – dc buck converters find applications in solar energy technologies where they are used in solar control charging systems, battery charging systems, drones, in the automotive industry where there is integration of the engine and dc-dc motor drives resulting in hybrid electric drives or vehicle’s. Conventional controllers that is the proportional derivative control (pid) have dominated the control engineering field from the time of invention, however, these controllers present increased overshoot and a long time to achieve steady-state conditions. In this regard since fuzzy logic has intelligent capabilities, then a fuzzy logic soft computing-based controller is proposed in this paper. A mathematical analysis of the dc-dc buck design is also given and the modeling of the fuzzy logic control algorithms that avoids mathematical analysis is also discussed. Fuzzy control is one of the soft computing tools that consists of the observation made by people and their decision based on non-numerical information is also discussed. The performance analysis of the fuzzy controller is determined under constant load and variable decreasing voltage conditions. The analysis and simulation of the dynamic response in closed-loop frequency response are conducted in the Simulink platform in Matlab. The proposition of control is executed on a dc-dc step down converter for an input of 12V. This proposed fuzzy logic control technique provides a dc – dc buck converter system with increased overall operating efficiency and a very stable output.

High-Performance Resonant Controller Implemented in the Discrete-Time Domain for Voltage Regulation of Grid-Forming Converters

Grid-forming converters (GFCs) offering sinusoidal voltage supply have been widely employed in a lot of applications. In this article, the dual-loop voltage–current control for GFCs is comprehensively approached. First, optimum tuning of the current loop is addressed to achieve the maximum enhanced active damping from the prospect of the developed equivalent plant, instead of the current loop, which has been the focus of the existing literature. Then, effectiveness of resonant controllers (RCs), i.e., proportional resonant and vector proportional integral, which are very popular for voltage regulation of GFCs, is addressed. It is found that for GFCs with a reasonably designed output filter, especially for high-power applications with a low switching frequency, a weekly damped region exists in the closed-loop frequency response with either of the two RCs employed, which can further result in constrained bandwidth and slow transient response. To solve this issue, a discrete RC is developed, which avoids the weekly damped region, and a fast response of the output voltage can be achieved. Experimental results have verified the effectiveness of the proposed controller for voltage regulation of GFCs.

Simultaneous damping and tracking control of a normal-stressed electromagnetic actuated nano-positioning stage

Normal-stressed electromagnetic actuated (NSEA) nano-positioning stage has become more and more promising in various fields due to its high actuation force density and large motion range. However, the intrinsic hysteresis of the actuator and the lightly-damped resonance of the mechanism hinder the stage for the high-accuracy and high-speed applications. To handle these two problems, the damping and tracking controllers are commonly adopted, as the inner and outer loops, respectively, to design a dual-loop controller. However, the existing sequential design approach limits the achievable performance of the controller. This paper proposes a simultaneous optimization approach for a dual-loop controller with the inner loop positive acceleration, velocity, and position feedback (PAVPF) damping controller and the outer loop proportional-integral (PI) tracking controller. The objective is to obtain a flat closed-loop frequency response with a large control bandwidth, and the parameters of the inner and outer loops are tuned simultaneously. Both the damping ratio and stiffness of the vibration mode are improved, and the obtained ± 3 dB control bandwidth exceeds the first resonant frequency of the open-loop system. Experiments are carried out on a custom designed NSEA nano-positioning stage. The tested bandwidth of the simultaneously optimized system agrees well with the theoretical one, and is 188.9% higher than that of the sequentially designed system. Step response tests, triangular wave tracking tests, and hysteresis reduction tests also demonstrate the effectiveness and advancement of the proposed approach.

Fractional-Order Approximation of PID Controller for Buck-Boost Converters.

Viability of a fractional-order proportional–integral–derivative (PID) approximation to regulate voltage in buck–boost converters is investigated. The converter applications range not only to high-power ones but also in micro/nano-scale systems from biomedicine for energy management/harvesting. Using a classic closed-loop control diagram the controller effectiveness is determined. Fractional calculus is considered due to its ability at modeling different types of systems accurately. The non-integer approach is integrated into the control strategy through a Laplacian operator biquadratic approximation to generate a flat phase curve in the system closed-loop frequency response. The controller synthesis considers both robustness and closed-loop performance to ensure a fast and stable regulation characteristic. A simple tuning method provides the appropriate gains to meet design requirements. The superiority of proposed approach, determined by comparing the obtained time constants with those from typical PID controllers, confirms it as alternative to controller non-minimum phases systems. Experimental realization of the resulting controller, implemented through resistor–capacitor (RC) circuits and operational amplifiers (OPAMPs) in adder configuration, confirms its effectiveness and viability.

A novel optimal PIλDND2N2 controller using coyote optimization algorithm for an AVR system

In this paper, a novel PIλDND2N2 controller is designed for an Automatic Voltage Regulator (AVR) in a power system and is studied in this paper. AVR is responsible for keeping the terminal voltage of a synchronous generator at a specified interval. The proposed control design is achieved by deploying for the first-time the coyote optimization algorithm (COA) in an AVR system by optimizing a novel objective function. A comparison is made among the proposed controller and FOPID, PID, PIDA and PIDD2 controllers optimized by others metaheuristic algorithms in the literature. The comparison is deducted in terms of transient response and disturbance rejection. From the simulations it is concluded that the proposed method outperforms other methods in the literature. Furthermore, the stability of the proposed design is examined via the location of the closed-loop poles and frequency response. Moreover, the robustness of the controller is tested under model uncertainties. In both tests the proposed method displays an outstanding performance.

Experimental Validation of Voltage Regulation in Buck Converters through Fractional-Order PID Approximation

Viability of a fractional-order PID approximation regulating voltage in buck converters through a single control loop is investigated. Fractional calculus approach is suggested due to it exhibits good robustness against parameter variations. The non-integer approach is integrated in the control strategy through a Laplacian operator biquadratic approximation to generate a flat phase curve in the system closed-loop frequency response, which results in the generation of the iso-damping characteristic. The synthesis and tuning process consider both robustness and closed-loop requirements to ensure a fast and stable regulation characteristic. Experimental data obtained with the resulting controller, which was easy implemented through RC circuits and OPAMPs in adder configuration, confirmed its effectiveness. Superiority of proposed approach, which is determined through a comparison with typical PID controllers, confirms its viability to be used in highly efficient converters, such as Silicon-Carbide ones.

Smart damping of skew composite plates using Murakami zig-zag function

The present work is aimed at deriving a finite element model for active constraining layer damping treatment (ACLD) of layered skew plates by incorporating zig-zag behaviour using a Murakami zig-zag function (MZZF). The ACLD in skew patch form comprises of 1–3 PZC material and viscoelastic material in the layer form placed on substrate skew plate. The overall skew substrate ACLD system deformation kinematics are derived using MZZF and the equations of motion for the same are derived by virtual work method. A MATLAB subroutine for the overall skew plate ACLD system has been developed to present the closed loop frequency responses by successful implementation of closed-loop feedback system. The substrate skew plates with different lamination schemes namely symmetric/antisymmetric cross-ply and antisymmetric angle-ply are considered to assess the damping behavior of the skew plates undergoing ACLD. Also, the piezo-fiber angle (obliquely reinforced) variation of the PZC layer on the damping responses of the skew plates have been thoroughly examined.

An Interactive Software Tool to Learn/Teach Robust Closed-Loop Shaping Control Systems Design

Models are always subject to uncertainty. This can come mainly from parameter uncertainty, reduced order dynamics, or unmodelled dynamics. The model uncertainty is a concept that is difficult to introduce in automatic control introductory courses. The mathematical formalization of many of the ideas necessary to introduce students to robust control is complex for most students, causing many students to get lost in the mathematics and do not understand the important control concepts. The closed-loop shaping control design methodology allows introducing the model uncertainty in a simple way. It has some very interesting characteristics from a teaching point of view, since it allows concentrating on shaping the closed-loop frequency response in order to obtain the desired performance and robustness. This paper presents the main features and functionality of RCLSD an interactive software tool developed by the authors for learning and teaching the robust closed-loop shaping control design methodology.

Design and Validation of a Two-Degree-of-Freedom Powered Ankle-Foot Orthosis with Two Pneumatic Artificial Muscles

Powered ankle-foot orthosis (PAFO) is a field of wearable robotics that improves the lives of people of old age or with physical impairments by aiding in the wearer's ankle joint movements. Most of the PAFOs developed thus far offer only one degree-of-freedom (dof), which uses the talocrural joint alone as the axis of rotation, where the emphasis is on moving forward. However, because this type of wearable robotics has evolved, developing PAFOs for functional rehabilitation has become necessary. This enhances the quality of walking rather than providing simple rehabilitation. The subtalar joint is responsible for the rotation of the inversion and eversion of the ankle, enabling balanced walking in humans, and is an important part of balance training for elderly people or stroke patient rehabilitation. Therefore, we developed a 2-dof PAFO that uses a calculated spatial formula of the subtalar joint based on anatomical data. In recognition of the fact that the pneumatic artificial muscle (PAM) can be used within the contracting range alone because of the instinct of the PAM, we analyzed the workspace of the fabricated PAFO through kinematic analysis and verified the possibility of using the PAFO during the gait cycle. Experiments were also conducted on the closed-loop force frequency response using a sliding mode control of the solenoid valve to validate the control characteristics. Lastly, clinical experiments with healthy subjects were conducted for validation in wearing conditions.

Design of a pressure modulator using fast-acting bistable valves

Fast-acting pneumatic valves, combined with a slip-control braking algorithm, have recently been used to improve the straight-line braking performance of an experimental heavy goods vehicle, on low friction roads, by 16%. This paper describes how the fast-acting valves, which were central to the aforementioned research, were designed for use on a commercial vehicle. Design equations, as well as a generalized design method, are first presented for the fast-acting bistable pneumatic valve. A pressure observer is developed to predict the brake chamber pressure in cases where a pressure transducer is mounted upstream. A simple fault detection algorithm is then introduced, which utilizes some of the calculations made in the pressure observer, and is shown to correctly identify faults on a real vehicle. Performance comparisons are made between the new modulator and a conventional heavy goods vehicle electro-pneumatic brake system. Closed-loop frequency response tests show that the control bandwidth of brake chamber pressure on a heavy goods vehicle can be increased from 1.5 Hz to 10 Hz using the new hardware.

Dq Synchronous Reference Frame Model of A Series–Series Tuned Inductive Power Transfer System

A control-oriented circuit model of an inductive power transfer system is needed to design a high-performance controller. In this article, a dq synchronous reference frame model of a series-series tuned resonant inductive power transfer system is proposed. A single-phase dq modeling technique for a resonant converter is used to derive the model. The proposed control-oriented model clearly demonstrates the cross- and mutual-coupling between the state variables of the wireless power transfer system. It is interesting to note that the proposed model is similar to a dq synchronous reference frame model of a three-phase induction motor. The well-known controller design methods, such as proportional-integral controller design, manipulated input decoupling, disturbance input decoupling, state observers, and disturbance observers, etc. can be extended to the inductive power systems with the proposed model. The large- and small-signal responses of the transmitter current versus its input voltage are identified. Considering the frequency response, a new transmitter current controller that has a control bandwidth of 500 Hz is designed to show the validity of the proposed model. The proposed model and the controller are evaluated using simulated and experimental results. The simulated open- and closed-loop frequency responses of the model agree well with the theoretical bode plots of them. Also, the experimental results show that the proportional-integral with feedforward input controller regulates the transmitter current within 1 ms for three conditions: a step change of the reference, a step change of the load, and a step change of the mutual-coupling.

In-Circuit Characterization of Low-Frequency Stability Margins in Power Amplifiers

Low-frequency resonances with low stability margins affect video bandwidth characteristics of power amplifiers. In this paper, a non connectorized measurement technique is presented to obtain the low-frequency critical poles at internal nodes of a hybrid amplifier. The experimental setup uses a high-impedance probe connected to a vector network analyzer to obtain a fully calibrated closed-loop frequency response that is identified to get the poles of the device at low frequency. Compared to previous connectorized solutions, the approach avoids the ad hoc insertion of extra RF connectors to access the low-frequency dynamics of the amplifier. In addition, it simplifies the characterization at multiple internal nodes, which is worthwhile for an efficient detection and fixing of critical low-frequency dynamics in multistage power amplifiers. The technique is first applied to dc steady-state regimes and compared to the connectorized approach on a single-stage amplifier. Next, it is applied to a three-stage amplifier to show its potential to detect the origin of the undesired dynamics and the most effective way to increase stability margin. Finally, the technique has been extended to the large-signal case to increase its usefulness for the design and diagnosis of high-power amplifiers.

Frequency Response Comparison of PI-Based FOC and Cascade-Free MPC using 1 kHz SVM Applied to PMSM drive

Abstract— This paper presents a 1 kHz SVM-FOC (Space Vector Modulation with Field Oriented Control) drive system for a Permanent Magnet Synchronous Motor, using different control strategies. Such strategies are internal model and frequency response designed PI (Proportional and Integral) controllers and a multivariable MPC (Model Predictive Control) controller using a state-space prediction model. This MPC method becomes interesting for improving the closed-loop speed frequency response, since it results in a cascade-free controller. The performance of each controller was evaluated in a qualitative manner through simulations and quantitatively by load torque and speed reference AC sweeps, generating dynamic stiffness curves and Bode diagrams for the utilized techniques. Results show that the MPC approach is useful for enabling fast dynamic responses with the reduced switching frequency, which reduces the drive system cost and improves its efficiency.

Nonlinear frequency response based adaptive vibration controller design for a class of nonlinear systems

Abstract Frequency response functions (FRF) are often used in the vibration controller design problems of mechanical systems. Unlike linear systems, the FRF derivation for nonlinear systems is not trivial due to their complex behaviors. To address this issue, the convergence property of nonlinear systems can be studied using convergence analysis. For a class of time-invariant nonlinear systems termed as convergent systems, the nonlinear FRF can be obtained. The present paper proposes a nonlinear FRF based adaptive vibration controller design for a mechanical system with cubic damping nonlinearity and a satellite system. Here the controller gains are tuned such that a desired closed-loop frequency response for a band of harmonic excitations is achieved. Unlike the system with cubic damping, the satellite system is not convergent, therefore an additional controller is utilized to achieve the convergence property. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller.