Passive Control Method Research Articles

Drag Reduction of Truck and Trailer Combination with Different Passive Flow Control Methods

In this study, drag force and surface pressure measurements were conducted on a 1/32 scaled truck-trailer combination model. The experimental tests were carried out between the ranges of 312×103- 844×103 Reynolds Numbers in a suction type wind tunnel. The aerodynamic drag coefficient (CD) and distribution of pressure coefficient (CP) were experimentally determined on the truck and trailer combination. The regions where has big pressure coefficients were determined on the truck-trailer by using flow visualizations. The aerodynamic structure of truck-trailer combination models was improved by passive flow control methods on 4 different models. By using newly designed spoiler on the model 1, drag coefficient was reduced 10.01 %. On the model 2, adding trailer rear extension with a spoiler, the reduction was obtained as 11.35 %. For the model 3 which is obtained adding side skirt to model 2, the improvement reached 18.85 %. The model 4 was composed of model 2 and a bellow between the truck and trailer. The drag force improvement was obtained as 22.80 % for model 4.

Novel passive flow control method using leading-edge prism-shaped cylinder: Performance enhancement of vertical-axis wind turbines

Due to periodic dynamic stall at low tip speed ratios (TSRs), vertical-axis wind turbines (VAWTs) experience notable performance challenges during rotation, which leads to fluctuations in torque and a decrease in energy capture. This research aims to boost the aerodynamic performance of Darrieus VAWTs by employing a leading-edge (LE) prism cylinder (PC) to enhance energy extraction. This novel small-scale device functions as a passive method for controlling flow separation, aiming to energize the boundary layer and adjust the pressure distribution on the blades. Its effectiveness depends on factors such as size, shape, and placement, necessitating careful optimization. A three-dimensional (3D) computational fluid dynamics (CFD) analysis, combined with Taguchi optimization and analysis of variance, is conducted to determine the optimal design parameters for the LE PC tool. This 3D CFD method captures the full complexity of flow dynamics, including vortex structures and wake behavior, leading to more accurate wind turbine performance predictions than two-dimensional (2D) CFD models. The results highlight the crucial role of PC size (Factor A), which contributes nearly 85% to the total contribution factor, while the angle of PC influence is minimal. The optimized rotor demonstrates a 36% increase in maximum average power coefficient (CP) compared to an uncontrolled rotor at TSR = 1.5. However, the effectiveness of this control method diminishes at higher TSRs because the blades encounter angles of attack below the critical stall angle throughout the rotation cycle, naturally preventing flow separation and making the flow separation control method unnecessary. The PC installed on the optimized blade delays flow separation to 55% of the blade chord length, compared to 40% for the base blade. Consequently, the rotor operates efficiently, ensuring consistent, and reliable power generation without flow separation issues.

Seismic isolation strategy via controlled soft first story with innovative multi-stage yielding damper: Experimental and numerical insights

While the presence of a soft story within a building is typically discouraged in structural engineering due to potential vulnerabilities, this research proposes a strategy that incorporates seismic isolation concepts by integrating a soft first story within the structural framework. This approach challenges traditional reluctance by demonstrating the potential benefits of such a configuration. The primary objectives are twofold: firstly, to diminish seismic responses and enhance structural resilience when subjected to earthquake forces, and secondly, to reduce construction costs as compared to conventional passive control methods. The seismic responses assessed and compared in this study encompass story displacements, story drifts, floor accelerations and base shear of the structure. Furthermore, an investigation is conducted into a replaceable or repairable shear fuse that serves as a controller in the Controlled Soft First Story (CSFS) strategy, namely, an innovative Multi-stage Steel Yielding Damper (MSYD). Notably, the numerical analysis of the introduced damper has been carried out, followed by rigorous validation testing under experimental conditions. This study elucidates the implementation of this strategy within the structural framework. The overarching principle behind employing the CSFS results in outcomes akin to those achieved with base isolation techniques. However, it distinguishes itself by significantly mitigating the construction costs around 70% associated with this system when juxtaposed with traditional base isolation systems.

Enhanced surface acoustic wave microfluidic performance through FDTS self-assembled monolayers on [formula omitted]

Microfluidics technology has been extensively applied in biochemical analysis and medical diagnostics, where precise and efficient control of microfluids is crucial. However, existing passive microfluidic control methods (e.g., microchannels) and active strategies (e.g., optical, thermal, magnetic field, and electrokinetic manipulation) are often hindered by complex device structures and operational uncertainties. Surface acoustic wave (SAW) microfluidic manipulation offers a promising alternative, providing flexible and efficient digital microfluidic control through the modulation of input signals. Nevertheless, the intrinsic hydrophilicity of substrates such as LiNbO3 results in inefficient microfluidic driving and jetting, primarily due to high surface tension. In this study, we employed chemical vapor deposition (CVD) to coat LiNbO3 substrates with 1H,1H,2H,2H-Perfluorododecyltrichlorosilane (FDTS) self-assembled monolayers (SAMs), creating hydrophobic surfaces with a contact angle of approximately 120°. In comparison to commercially available Glaco hydrophobic coatings, which reduce SAW amplitude by approximately threefold and increase substrate temperature by up to 1.5 times, FDTS SAMs exhibit negligible impact on SAW properties. Furthermore, when compared to untreated SAW devices, FDTS SAMs-coated devices demonstrated a sixfold increase in droplet driving speed under low power input (e.g., 0.5 W), enabling faster and more precise liquid jetting at velocities reaching 5 m/s. This work highlights the potential of FDTS SAMs in enhancing the performance of SAW-driven microfluidic devices, particularly in applications requiring high-efficiency droplet manipulation.

Optimization Design of Bionic Leading-edge Protuberances on Horizontal Axis Wind Turbine Blades

Abstract The complex operating environments of horizontal axis wind turbines has made the phenomenon of blade flow separation more obvious. As a passive flow control method, the bionic humpback whale leading-edge protuberances have been shown to effectively enhance the performance of the wind turbine. This study employs a multi-objective genetic algorithm and Computational Fluid Dynamics method to analyse the impact of leading-edge protuberances on the aerodynamic performance and flow characteristics of the blades. The results indicate a significant improvement in blade performance after optimization in the wind turbine’s output power. The streamwise vortices generated by the bionic protuberances not only reduce the suction surface pressure, but also suppress the spanwise flow over the blade surface. The length of the flow separation Region is reduced from 0.410 to 0.368 radius. In the process of wind speed change, the tangential forces on the bionic blade exhibit a wave-like variation. The bionic protuberance alters the pressure coefficient of the position. Compared with the original blade, the pressure coefficient of the trough sections on both sides of the bionic blade protuberance is improved. In this study, the bionic protuberance applied to the leading-edge of horizontal-axis wind turbine blades is proposed for the first time, and holds practical value for guiding practical applications.

Vibration Control for Laminated Composite Spherical-Cylindrical-Combined Shells: Theory and Experiment

Considering the structural damage and instability due to extensive vibrations, the present investigation focuses on the dynamic characteristics analysis and vibration control for aerospace structures such as rocket stages and aircraft cowling, modeled as laminated composite spherical-cylindrical-combined shells (SCCSs). The theoretical model of the SCCSs is established by a series of artificial connection and boundary springs. The proposed method’s validity is confirmed through finite element analysis and experimental validation. Nickel-titanium-steel wire ropes (NiTi-STs) are then introduced as a passive vibration control method for the SCCSs. Both circumferential and axial NiTi-ST laying schemes demonstrate good vibration control capabilities on the SCCSs. For similar lengths of NiTi-STs, the vibration control effect of circumferential laying schemes is superior to that of the axial one. Furthermore, the vibration control effect of the circumferential schemes is found to be dependent on the number and positioning of NiTi-STs. The influence of the NiTi-ST structural parameters on the vibration control performance is also analyzed; adjusting the structural parameters appropriately is helpful to improve the vibration reduction effect.

Prediction and Control of Broadband Noise Associated with Advanced Air Mobility—A Review

This review presents an overview of advanced air mobility broadband noise (BBN) prediction and control techniques, highlighting significant advancements in various prediction models. Methods such as the semi-empirical Brooks–Pope–Marcolini (BPM) model, analytical Amiet model, and time-domain models based on the FW-H equation have been extensively studied. Machine learning (ML) shows promise in BBN prediction but requires extensive data training and application to noise source mechanisms. Passive control methods, such as leading and trailing edge serrations and blade tip designs, have been partially successful but often compromise the aerodynamic performance. Active control methods, like suction and blowing control, trim adjustments, and dielectric barrier discharge (DBD) plasma actuators, show great potential, with the latter two being particularly effective for reducing BBN in thin propeller structures. Overall, while progress has been made in understanding and predicting BBN, further research is needed to refine these methods and develop comprehensive noise control strategies. These advancements hold significant promise for effective and efficient noise mitigation in future AAM vehicles.

An experimental investigation into the influence of the micro vortex generator on the leading stability of cloud cavities around a hydrofoil

The objective of this paper is to investigate the effect of a passive control method on the leading stability of a cloud cavity around a hydrofoil. Two differently positioned micro vortex generators (mVG) are installed on the leading edge (LE) of a National Advisory Committee for Aeronautics 66 hydrofoil. The structural parameters of mVG-1 are the same as those of mVG-2, but closer to the LE of the hydrofoil. A high-speed camera is employed to capture the transient evolution of cavitating flow. The results show that the cloud cavities on the baseline hydrofoil are divided into the hybrid cavity mode (α = 6°) and the fingerlike cavity mode (α = 8°–12°), relying on the cavity LE structure. The hybrid cavity consists of coupled traveling bubbles and fingerlike cavities, dominated by fingerlike cavities. The fingerlike cavity is attached to cavities with only a single form of LE. The hybrid cavity is replaced by fingerlike vortex cavitation on the mVG hydrofoil, leading to a fixed incipient position of the cavity. Fingerlike cavity structures on the three hydrofoils are generated by different mechanisms. The fingerlike vortex cavity of the mVG-1 hydrofoil is induced by the mVG, whereas the other two hydrofoils are induced by boundary layer separation and spanwise.

On the Optimum Distribution of Multiple Helmholtz Resonators for Annular Combustors

Abstract The combustors of many modern land-based gas turbines and aero-engines are annular. This kind of combustors often suffer from thermoacoustic oscillations, with the occurrence of mostly the circumferential first-order, second-order and third-order oscillation modes in the annular combustion chamber. To solve this problem, passive control methods are widely used adding passive acoustic dampers such as Helmholtz resonators (HRs). Depending on the type and number of HRs, and the possible positions over the circumference to install them, there could easily have millions, or even billions, of possible arrangment patterns. Finding a good design is the key to solve this problem. In this paper, we perform a theoretical and numerical study of an annular combustor installed with multiple types of HRs over the circumference. Firstly, a simple annular duct with arbitrary distributions of these HRs is studied analytically by solving the nonlinear eigenvalue problem of a 1D network model. Based on the results of the analytical method, the impact of the HRs on the acoustic modes of the combustion chamber is studied and the optimum arrangement of multiple resonators is obtained. This arrangement usually gives a null (or small) mode splitting strength and a good damping effect. Finally, we apply the optimum arrangement to damp the thermoacoustic modes that have been captured by numerical simulation for a real annular combustor. We use numerical simulations based on solving the 3D Helmholtz equation in COMSOL to verify the feasibility of the optimum arrangement.

Aeroacoustic Coupling in Rectangular Deep Cavities: Passive Control and Flow Dynamics

Deep cavity configurations are common in various industrial applications, including automotive windows, sunroofs, and many other applications in aerospace engineering. Flows over such a geometry can result in aeroacoustic coupling between the cavity shear layer oscillations and the surrounding acoustic modes. This phenomenon can result in a resonance that can lead to significant noise and may cause damage to mechanical structures. Flow control methods are usually used to reduce or eliminate the aeroacoustic resonance. An experimental set up was developed to study the effectiveness of both a cylinder and a profiled cylinder positioned upstream from the cavity in reducing the flow resonance. The cavity flow and the acoustic signals were obtained using particle image velocimetry (PIV) and unsteady pressure sensors, respectively. A decrease of up to 36 dB was obtained in the sound pressure levels (SPL) using the passive control methods. The profiled cylinder showed a similar efficacy in reducing the resonance despite the absence of a high-frequency forcing. Time-space cross-correlation maps along the cavity shear layer showed the suppression of the feedback mechanism for both control methods. A snapshot proper orthogonal decomposition (POD) showed interesting differences between the cylinder and profiled cylinder control methods in terms of kinetic energy content and the vortex dynamics behavior. Furthermore, the interaction of the wake of the control device with the cavity shear layer and its impact on the aeroacoustic coupling was investigated using the POD analysis.

Reactor power control system design and dynamic simulation for load maneuvers over full range and entire lifetime of an integrated supercritical CO2 reactor plant

Due to advantage of high efficiency, low carbon, and flexible operation, the integrated supercritical CO2 reactor plant has promising prospect in energy supply. This paper aims to clarify performance of the reactor plant and establish a reactor power control strategy through numerical modeling. Firstly, performance on separated components is evaluated to provide guidance for control strategy development. Secondly, influence of control methods, controller schemes, and saturation models on control strategy are discussed. Thirdly, dynamic response of reactor plant with proposed control strategy is confirmed via load change transients. Results show that passive control method is infeasible at EOL and load demand below 50 %FP, and active control method must be considered. The proposed control strategy adopts coupled temperature-channel and power-channel scheme and soft saturation model. It ensures safe operation of the plant over full load range in whole lifetime. These results can provide helpful guidance on part-load operation for this system.

The Performance and Fabrication of 3D Variable Cross-Section Channel for Passive Microfluidic Control.

Passive fluid control has mostly been used for valves, pumps, and mixers in microfluidic systems. The basic principle is to generate localized losses in special channel structures, such as branches, grooves, or spirals. The flow field in two-dimensional space can be easily calculated using the typical Stokes formula, but it is challenging in three-dimensional space. Moreover, the flow field with periodic variable cross-sections channeled of polyhedral units has been neglected in this research field due to previous limitations in manufacturing technology. With the continuous progress of 3D printing technology, the field of microfluidic devices ushered in a new era of manufacturing three-dimensional irregular channels. In this study, we present finite analysis results for a periodic nodular-like channel. The experiments involve variations in the Reynold number (Re), periodic frequency, and comparative analyses with conventional structures. The findings indicate that this variable 3D cross-section structure can readily achieve performance comparable to other passive fluid control methods in valve applications. A 3D model of the periodic tetrahedron channel was fabricated using 3D printing to validate these conclusions. This research has the potential to significantly enhance the performance of passive fluid control units that have long been constrained by manufacturing dimensions.

Experimental investigation on the aerodynamics and flow patterns of a 5:1 rectangular cylinder with spoilers

The current study experimentally investigates a passive control method for the flow field by placing spoilers symmetrically on the leading edge of a 5:1 rectangular cylinder. The Reynolds number (Re) is based on the inflow velocity and the height of the model. The length of the spoiler is equal to the span length of the model, and the width and angle are defined as w and α. At Re = 1.07 2.50×104, the surface pressure distribution of the model is obtained to initially investigate the effects of α and w on the aerodynamic characteristics. Based on the aerodynamic results, some cases are selected to reveal the control mechanism using the particle image velocimetry (PIV) technique. The proper orthogonal decomposition (POD) is adopted to analyze the POD modes and instantaneous flow. The results show that the spoiler with a certain α can suppress the aerodynamic forces of the model. Spoilers with a relative angle of 247.5° significantly reduce CL′ by 75 % and slightly reduce CD¯ by 5.5 %. Also, its TKE and RSS values are reduced by 56 % and 57 %, respectively. The PIV visualization shows that the spoiler affects the flow separation at the leading edge. Then, the rolling and interactions of shear layers are suppressed, making them tend to be parallel. Besides, spoilers with a relative angle of 67.5° almost eliminate the flow separation.

Numerical simulation of wake flow around two square cylinders through passive control method

Two-dimensional numerical simulations are performed to study the effect of height of control plates placed at the downstream location in a vertical direction of a channel for flow past two inline square cylinders. The numerical method used is the lattice Boltzmann method (LBM) and Reynolds number is kept constant at Re = 150 (Re = Uinf d/ν) for fixed gap spacing g = 3.5 (g = s/d). The height of the control plate varies from h = 0.1 to 8. First, the validity of code for the present problem and suitable grid points are checked along the selection of uniform inflow velocity. After that verification, the numerical simulations are performed to obtain the results under the effect of height of control plates using the passive control method. Calculated results are, in terms of vorticity contour, drag and lift coefficients, pressure contour, energy spectrum, and force statistics. Under the discussion of vorticity contour visualization, we obtained six types of flow mode and named them according to flow behavior and their characteristics. In pressure contour, it is visualized that the maximum pressure occurred at near the upstream position of the first cylinder as well as the upper and lower edge of the main cylinder as compared to the downstream cylinder and control plate, but at some position inside the domain, pressure contour contained negative values as well in between the gap of two square cylinders and control plate. In force statistics, we computed the values of Cdmean, Cdrms, Clrms, and St. Mean drag coefficients for both upstream cylinder (C1) and downstream cylinder (C2) are increased as the height of the control plate increased from 0.1 to 1.5, but as the height of the control plate reached its maximum value, the value of Cdmean turned toward the decline. The maximum value of Cdmean obtained at h = 2.25 and the minimum value occurred at h = 8. For cylinder C2, negative values for some selected heights such as h = 0.1–1.25 and h = 4–8 are also observed because of thrust. The value of the Strouhal number for both the cylinders C1 and C2 are similar at h = 0.1–4.5, but at h = 5, the values of the Strouhal number differ for both cylinders, but at the largest values of control plate's height, i.e., h = 6–8, the Strouhal number contains zero values for both cylinders C1 and C2. At these zero values of the Strouhal number, in vorticity contour jet type of flow mode is observed at h = 6–8, as a new flow mode, which is not identified before in the passive control method for flow past two or more square cylinders.

Vibration Reduction by a Partitioned Dynamic Vibration Absorber with Acoustic Black Hole Features

Vibration quality is a vital indicator for assessing the progress of modern equipment. The dynamic vibration absorber (DVA) based on the acoustic black hole (ABH) feature is a new passive control method that manipulates waves. It offers efficient energy focalization and broad-spectrum vibration suppression, making it highly promising for applications in large equipment such as aircraft, trains, and ships. Despite previous advancements in ABH-DVA development, certain challenges remain, particularly in ensuring effective coupling with host structures during control. To address these issues, this study proposes a partitioned ABH-featured dynamic vibration absorber (PABH-DVA) with partitions in the radial direction of the disc. By employing a plate as the host structure, simulations and experiments were conducted, demonstrating that the PABH-DVA outperforms the original symmetric ABH-DVA in terms of damping performance. The study also calculated and compared the coupling coefficients of the two ABH-DVAs to uncover the mechanism behind the enhanced damping. Simulation results revealed that the PABH-DVA exhibits more coupled modes, occasionally with lower coupling coefficients than the symmetric ABH-DVA. The influence of frequency ratio and modal mass was further analyzed to explain the reasons behind the PABH-DVA's superior damping performance. Additionally, the study discussed the impact of the number of slits and their orientation. This research further explains the coupling mechanism between the ABH-DVA and the controlled structure, and provides new ideas for the further application of ABH in engineering.

Hybrid compliant control with variable-stiffness wrist for assembly and grinding application

This research presents a novel robot system that combines active and passive components to enhance compliance and dependability. The system is based on a continuous variable stiffness wrist. A wrist was created that met the requirements and a combination of active and passive control methods was suggested to insert and regulate forces effectively. The control strategy is based on the Cosserat rod model, with the fundamental concept being calculating the position and orientation of the component using data on the force exerted during contact between the parts and the stiffness of the contact between the shaft and hole components. This process converts the hard assembly into a flexible contact. Compliance is monitored via force and vision sensors, which allows for the shaft-hole assembly operation to be carried out even with attitude alignment problems, resulting in a notable decrease in the precision needed for component alignment. Initially, the camera supplies the first positional data of the shaft component for the robotic system. In addition, the performance of the wrist with variable stiffness is evaluated in terms of stiffness. Additionally, the calculation of relative deformation between components is examined using contact force information. Moreover, a robust active/passive hybrid insertion control technique, which relies on contact force, is proposed. Finally, the shaft-hole assembly task substantiates the necessity for contact force monitoring in the insertion assembly process. This control technique has demonstrated its efficacy in ensuring passive-compliant assembly performance. Furthermore, the variable stiffness wrist has been employed in robotic grinding for surfaces with curved contours to validate its effectiveness.

The groove effect on wake characteristics of rotating cylinders

In the present study, active and passive flow control methods have been implemented to investigate their effects on the wake flow structures of a circular cylinder. Grooves having circular, rectangular, and triangular cross sections have been applied to the cylinders exposed to the rotation rates, α, from 0 to 0.79. The experiments have been conducted by particle image velocimetry at a Reynolds number of Re = 5 × 103. The contour graphics of time-averaged results have been presented. Moreover, the variations in velocity profiles have also been depicted. The experimental results revealed significant variations for flow patterns, wake structures, and turbulence parameters due to the effects of both groove geometries and rotational motion. In the stationary cases, for turbulence intensity, the circular grooved cylinder exhibited a 15% increase, while the triangular grooved cylinder showed a slightly higher increase of around 20% compared to that of the bare cylinder (BC). Conversely, in non-stationary cases, the rectangular grooved cylinder displayed the most prominent reduction in turbulence intensity, decreasing by approximately 10% compared to that of the BC. The groove type has considerably affected the flow structures of the wake regions, especially for the lower rotation rates.

Effect of leading-edge protuberances on swept wing aircraft performance

Stall is a complex phenomenon in aircraft that must be suppressed during flight. As a novel passive control method, bionic leading-edge protuberances (LEPs) have attracted widespread interest, particularly for delaying stall. Bionic protuberances at the leading edge of airfoils have been designed to control stall and increase the stability of unmanned aerial vehicles during operation, and it is the flow control mechanism associated with this application that is investigated in this study. First, numerical simulations are conducted to obtain the aerodynamic characteristics of original and bionic airfoils based on the S1223 large-lift airfoil. Next, the impact of the LEP amplitude is investigated. Finally, a vortex definition parameter, the Liutex vector, is utilized to analyze the influence of LEPs on vortices. The results show that bionic LEPs inspired by those on humpback whale flippers can improve the aerodynamic performance of airfoils under the extreme conditions that exist after stall, resulting in an ∼22% increase in the lift–drag ratio. LEPs are found to segment the flow field near the wing surface. The flow becomes bounded between adjacent protuberance structures, significantly inhibiting the development of flow separation and providing a drag reduction effect. This study thus provides a new approach for improving aircraft performance.

A mode localization inspired vibration control method based on the axially functionally graded design for beam structures

Vibration control plays a vital role in engineering structures, especially for low-frequency range, because designing structures with small dimensions makes it difficult to control large-wavelength vibrations. The present study seeks another road to realize low-frequency vibration control from the view of the real vibration responses. Similar to mode shapes, deflection modes are the main distributions of vibration amplitudes on structures in low frequency. Therefore, they are also essential vibration characteristics of structures. This paper proposes an effective passive vibration control method under both non-resonant and resonant excitations based on deflection mode theory and optimal algorithm. In fact, it is just like an axially functionally graded design for structures. The equations of motion for non-uniform beam structures are formulated by Hamilton’s principle. Firstly, a desired deflection mode is artificially designed, and the beam structure is discretely divided into subunits. Then, by adjusting the thickness or elastic modulus of each subunit to make the deflection mode of the beam coincide with that of the desired one. This process is completed by the genetic algorithm (GA). After that, by experimental and simulation analyses, the deflection mode of the optimally designed beam structures coincides with that of the desired one. Therefore, the present vibration control method is verified to be correct and effective.

Hybrid passive vibration control of lightweight manipulators

Passive vibration control methods in the literature are known to be highly sensitive to dynamic system parameters and are generally applied one by one. Therefore, their effectiveness in suppressing vibration control is limited. In this work, hybrid passive control (HPC) by integrating the Posicast control (PC) and the motion parameters-based control (MPC) is developed to suppress the during-motion vibrations (DMV) and residual vibrations (RV) of a single-link lightweight manipulator with a payload. PC is designed as a three-step cycle using the first natural frequency and damping ratio of the manipulator. MPC is designed by determining the time parameters of the motion profiles based on the first natural frequency of the manipulator. HPC simulations are performed on MATLAB, creating a Simscape model of the manipulator. Then, the proposed control method is tested in experiments. The prepared hybrid motion inputs actuate the servomotor while the displacements are measured, using a laser sensor at the tip of the manipulator. DMV and RV responses and their RMS values reveal that suppressing the vibration amplitudes efficiently. MPC is mostly effective in eliminating RV, whereas PC is sensitive to DMV as well. HPC combines these methods by eliminating their disadvantages and highlighting their advantages. Moreover, it is also successful in cases where the deceleration time of the trapezoidal input signal is single times half of the natural period, unlike MPC.