Linear Design Method Research Articles

Response-spectrum-based design method for gain-scheduling control of active base-isolated structures with nonlinear viscous dampers

The response-spectrum-based design method has been developed for linear active base-isolation to eliminate numerical simulations and trial-and-error testing. On the other hand, gain-scheduling is an effective control method for nonlinear systems and provides a way to apply linear system design methods. In this paper, we extend the response-spectrum-based design method to incorporate the gain-scheduling control strategy for active base-isolated structures with nonlinear viscous dampers (NVDs), aiming to effectively control these structures and simplify the design process. The gain scheduling of the controller is achieved based on the linear time-varying viscous coefficient of NVDs. The active base-isolated structure with NVDs is described as a pseudo linear parameter varying model. The stability of the system is proven and analyzed using a common Lyapunov function. Moreover, this paper proposes a control-force spectrum for estimating the maximum required control force without numerical simulations. Numerical examples are used to validate the effectiveness of the proposed spectra. Finally, we also detail the design process and verify the design method through a design example. The results show that this method directly determines the design parameters from the spectra and satisfies the design criteria of response and control force without numerical simulations, offering a promising design approach for active control of buildings with nonlinear energy dissipating devices.

Equivalent continuous method based novel design of a nonlinear TMD with piecewise stiffness

Tuned mass Dampers (TMDs) are extensively used passive control devices for high-rise buildings to mitigate undesirable responses. In practice, limit devices are frequently applied due to the large displacement of TMD, resulting in the emergence of piecewise nonlinearity. In this study, a TMD with piecewise stiffness (PSTMD) is developed to investigate the piecewise nonlinearity, including piecewise linear stiffness (PLS) and piecewise nonlinear stiffness (PNS). Initially, a novel equivalent continuous method (ECM) is proposed based on the principles of the least squares method (LSM) to approximate the PSTMD using a nonlinear TMD with Duffing stiffness. The equivalent nonlinear TMD is proven to be accurate enough to approximate the PSTMD. Subsequently, frequency response analysis is conducted on the PSTMD designed by linear method, results indicate that the linear method fails to design PSTMD. Thirdly, the optimal parameters of PSTMD are determined based on the ECM and the improved design method for nonlinear TMD proposed by the author. Results indicate that this novel design method effectively enhances the performance of PSTMD and mitigates the effect of piecewise nonlinearity. Finally, the influence of parameters of PSTMD on the optimal tuning frequency is investigated. The influence of damping ratio of PSTMD is explored by numerical simulation, with results indicating that employing the damping ratio suggested by traditional linear design method as the optimal parameter is reasonable. In summary, the novel method proposed in this study holds significance for the engineering design of TMDs with piecewise characteristics.

Practice-oriented controller design of a simple nonlinear system

The paper analyses and illustrates the design of a constrained gain scheduling for a simple non-linear hydraulic system based on automatic-reset controller. The main objective is to explain the basics of gain-scheduling control in a simple way so that it can be understood by computer programmers working in the field of automatic control. The study is based on small deviations from the selected operating points that allow the use of linear design methods. In contrast to linearization-based design methods, where the control action is calculated by integrating small control increments, the new control output is obtained by adding the calculated small increments to the operating point values. Another innovative aspect is the introduction of a gain-scheduled automatic-reset controller. This is the oldest and the simplest control solution including a disturbance observer based on ultra-local models and accurate even in steady-states.

An Objective Holographic Feedback Linearization Based on a Sliding Mode Control for a Buck Converter with a Constant Power Load

As a typical load, the constant power load (CPL) has negative impedance characteristics. The stability of the buck converter system with a mixed load of CPL and resistive load is affected by the size of the CPL. When the resistive load is larger than the CPL, the buck converter with the output voltage as an output function is a non-minimum phase nonlinear system, because its linear approximation has a right-half-plane pole. The non-minimum phase characteristic limits the application of many control techniques, but the objective holographic feedback linearization control (OHFLC) method is a good control strategy that can bypass the non-minimum phase system and make the system stable. However, the traditional OHFLC method, in designing the controller, generally uses a linear optimal quadratic design method to obtain a linear feedback control law. It requires a state quantity component with a one-order relative degree to the system. But it is not easy to find such a suitable state quantity with a one-order relative degree to the system. In this paper, an improved OHFLC method is proposed for Buck converters with a mixed loads of CPL and resistive loads, using the sliding mode control (SMC) theory to design the controller, so that the output state quantity components with different relative degrees to the system can be used in the holographic feedback linearization method. Finally, the simulation and experimental results also demonstrate that this method has the same, or even better, dynamic response performance and robustness than the traditional OHFLC method.

Robust Observer-Based Visual Servo Control for Quadrotors Tracking Unknown Moving Targets

This article addresses the image-based control problem of a quadrotor for tracking an unknown moving target under external disturbances. Based on the continuous observer design, a constructive image-based visual servoing (IBVS) geometric tracking control strategy is proposed and utilized. First, a higher order sliding mode observer is designed based on image dynamics for continuous estimation of unmeasurable linear velocities and time-varying disturbances. Furthermore, exploiting the linear quadratic regulator optimal design method, an outer loop IBVS controller is proposed such that the position of the quadrotor converges to the desired tracking pattern. Next, an inner loop geometric controller is designed using Lie algebra functions to regulate the attitudes. Based on the Lyapunov stability theory, it is rigorously proven that the proposed IBVS geometric controller achieves asymptotic stability. Finally, the effectiveness and robustness of the proposed approach against uncertain targets, time-varying disturbances, and large initial inclination angles are demonstrated through numerical simulations and experiments.

Selection of Optimum Land Leveling Design Method for Surface Irrigation

Land leveling or land grading of surface irrigated fields improve irrigation water distribution and application efficiencies, conserve water and increases crop productivity. Land formation for irrigation face many constraints (ensuring proper slopes, prevention of flood, ensuring canal water command over the field, optimizing earthwork, minimizing truck travel distances, proper equipment utilization). Design engineers traditionally, perform site formation design manually by plane shape, least squire or linear programming methods. Such methods are with different characteristics. The main objective this study is to select and compare performance of these three design methods for proper land leveling design. Consequently, the basic theory of these alternative design methods are reviewed and their performance using data surveyed from five fields in Khartoum North-Sudan, each with different soil surface topographic configurations, is analyzed. The statistical analysis revealed that the linear programming method is the most appropriate design method. Employing the linear programming design method revealed that design slopes in row and cross row directions are within the acceptable range (0.1 to 0.5, the ratio of Cut/fill volumes is within the recommended range (1.1 to 1.3), uniformity of distribution of design elevations of grid points are acceptable and within the target limits (80%), while their deviation is at 80% of grid points around the mean before leveling.

Real-Time Level Control of Spherical Tank Process using Gain Scheduled PID Controller

The objective of this paper is to maintain the level inside the process tank in a desired value. The real time implementation of the process is designed and implemented in MATLAB. Gain scheduled PID controller is designed to enhance the performance of the conventional PID controller for nonlinear spherical tank process. It is based on linearization of the nonlinear model around selected operating points. The linear design methods are applied at each region in order to arrive at a set of linear control laws. How to cite this article: Vadivazhagi S, Prabha KS, Vinodhini M et al. Real-Time Level Control of Spherical Tank Process using Gain Scheduled PID Controller. J Adv Res Instru Control Engi 2022; 9(3&4): 1-7. DOI: https://doi.org/10.24321/2456.1398.202201

Optimal Sliding Mode Preview Repetitive Control for Three-Phase Z-Source Inverters

Aiming at high output voltage and obvious current fluctuation of the off grids inverters with unbalanced and nonlinear loads, a compound control strategy of sliding mode controller and optimal preview controller based on Z-source inverter (ZSI) is proposed. ZSI can boost the pressure and improve the system energy conversion rate through by combining the state with the linear quadratic design method of optimal control. The preview controller is introduced in the feedforward compensation link. With the help of difference operator, an extended state error system covering the target value signal and lag link feedback is designed. The optimal preview repetitive control (PRC) is transformed into a linear quadratic regulation matter of the discrete systems. Furthermore, a preview repetitive controller is obtained by using the Lyapunov method, linear matrix inequality, and the design method of optimal controller, which can realize sliding mode control, state feedback, repetitive control, and preview compensation. Finally, a 10 kV A prototype is built to verify the effectiveness of the proposed strategy.

Universal Graph Filter Design Based on Butterworth, Chebyshev, and Elliptic Functions

Graph filters are crucial tools in processing the spectrum of graph signals. In this paper, we propose to design universal IIR graph filters with low computational complexity by using three kinds of functions, which are Butterworth, Chebyshev, and elliptic functions, respectively. Specifically, inspired by the classical analog filter design method, we first derive the zeros and poles of graph frequency responses. With these zeros and poles, we construct the conjugate graph filters to design the Butterworth high-pass graph filter, Chebyshev high-pass graph filter, and elliptic high-pass graph filter, respectively. On this basis, we further propose to construct a desired graph filter of low pass, band pass, and band stop by mapping the parameters of the desired graph filter to those of the equivalent high-pass graph filter. Furthermore, we propose to set the graph filter order given the maximum passband attenuation and the minimum stopband attenuation. Our numerical results show that the proposed graph filter design methods realize the desired frequency response more accurately than the autoregressive moving average graph filter design method, the linear least-squares fitting-based graph filter design method, and the Chebyshev FIR polynomial graph filter design method.

Economic Operation of Droop-Controlled AC Microgrids

Linear droop control is a standard approach for the decentralized operation of AC microgrids. While the traditional design of the real and reactive power droop functions does not consider economic aspects, recent approaches present modifications to enable least-cost operation. This paper proposes mixed-integer conic programming (MICP) for computing the real and reactive power droop parameters from a stochastic optimization framework that captures several snapshots of the microgrid’s operation. The model permits distributed generation to switch between grid-forming and grid-feeding modes. Unlike previous works, MICP provides droop parameters that are globally optimal for the design scenarios. Numerical results show that using traditional linear cost-based droop design methods may result in voltage magnitude violations. In contrast, the proposed method gives a solution free of violations and is yet more economical.

Latest findings on the behaviour factor q for the seismic design of URM buildings

Recent earthquakes as the 2012 Emilia earthquake sequence showed that recently built unreinforced masonry (URM) buildings behaved much better than expected and sustained, despite the maximum PGA values ranged between 0.20–0.30 g, either minor damage or structural damage that is deemed repairable. Especially low-rise residential and commercial masonry buildings with a code-conforming seismic design and detailing behaved in general very well without substantial damages. The low damage grades of modern masonry buildings that was observed during this earthquake series highlighted again that codified design procedures based on linear analysis can be rather conservative. Although advances in simulation tools make nonlinear calculation methods more readily accessible to designers, linear analyses will still be the standard design method for years to come. The present paper aims to improve the linear seismic design method by providing a proper definition of the q-factor of URM buildings. These q-factors are derived for low-rise URM buildings with rigid diaphragms which represent recent construction practise in low to moderate seismic areas of Italy and Germany. The behaviour factor components for deformation and energy dissipation capacity and for overstrength due to the redistribution of forces are derived by means of pushover analyses. Furthermore, considerations on the behaviour factor component due to other sources of overstrength in masonry buildings are presented. As a result of the investigations, rationally based values of the behaviour factor q to be used in linear analyses in the range of 2.0–3.0 are proposed.

Evaluating heat pump system design methods towards a sustainable heat supply in residential buildings

Aiming at an emission-free building energy supply, air-source heat pump systems (HPSs) are promising to replace conventional technologies such as gas boilers. Currently, the overall costs of HPSs are higher than the costs for conventional systems, inhibiting HPS market penetration in existing buildings. Increasing the profitability of HPSs by reducing overall costs simultaneously decreases buildings’ emissions. Total costs consist of investments (depending on the design) and operating costs (depending on the operation). While design and operation are mutually dependent, it is necessary to consider them at once in the design stage to exploit the full potential of HPSs. However, in the literature, there is no general framework to consider operation already within an overall design process. To close this gap, we develop a framework called X-HD enabling the comparison of three different design methods: a heuristic method based on the normative standard DIN EN 15450 (1: HSM), a mixed-integer linear programming optimization design method (2: OBM), and a simulation-based design method (3: SBM). All three methods design reliable HPSs consisting of a heat pump, an auxiliary heater, and two thermal energy storages: one for space heating and one for domestic hot water. A single-family house serves as a case study representing a part of the German building stock, and the annuity method is applied to evaluate the economic efficiency. While the design according to OBM (2) and SBM (3) outperform HSM design (1) by 3 % in annuity and 14 % in operating costs, HSM design (1) offers easy and fast handling. The results highlight the necessity of considering HPSs’ operation already in the design process. Although the OBM design (2) reveals the highest cost-saving potential, we recommend the SBM design (3) due to the consideration of nonlinear interdependencies, which occur during operation. We suggest coupling simulation-based design methods with an optimization method to determine optimal solutions while still integrating nonlinear system behavior for future work. Doing so, we pave the way towards an emission-free building sector based on HPSs.

Analytical analysis for optimizing mass ratio of nonlinear tuned mass dampers

To reduce the adverse vibrations of buildings, tuned mass dampers (TMDs), which are the most representative passive control devices, have been widely used and studied in aerospace, machinery, civil engineering, and other fields for many years. Most scholars used to treat the TMD as a linear damper, but they show some nonlinear characteristics owing to the use of limit devices and large displacements. It is necessary to consider the nonlinear coefficient of the TMD when designing its parameters. In this study, the mass ratio of the TMD was optimized by considering the nonlinear coefficient of the TMD. The complex variable average method and multiscale method were used for analysis. A mass ratio interval was found on the “\(\varepsilon - N_{2}\)” curve in which modulation response can occur, and then an analytical method for obtaining the optimal mass ratio of TMD was derived based on this phenomenon. The numerical results showed that taking the midpoint of this mass ratio interval as the optimal mass ratio can yield a better damping effect and robustness than using the traditional linear design method.

Design Analysis and Experimental Research of Multi-Segment Linear Reflector

The parabolic reflector provides one of the common sound wave convergence methods in acoustic engineering. To reduce the difficulty of fabricating large-size reflectors and improve the convergence effect, this paper proposes a multi-segment linear reflector design method. Through the normal vibration radiation analysis of the flextensional transducer shell, the reflector interface reflection was optimized, the reflection effect was improved and the reflector size was reduced. The transmission theory was used to analyze the impact of different material parameters and sound wave frequency on the reflector transmission coefficient, and the gain effect of the multi-segment linear reflector was further tested. The research results show that the reflector has a significant gain effect in the test frequency band of 20∼100Hz, and the gain at 70Hz I reaches the maximum of 11.2dB.

Exponential passive filter design for switched neural networks with time-delay and reaction-diffusion terms

This paper investigates the problem of exponential passive filter design for switched neural networks with time-delay and reaction-diffusion terms. With the aid of a suitable Lyapunov–Krasovskii functional and some inequalities, a linear matrix inequality-based design method is developed that not only makes the filtering error system exponentially stable but also forces it to be passive from external interference to output error. Then, the filter design is extended to the complex-valued case via separating the system into real-valued and complex-valued parts. Finally, a numerical example is utilized to illustrate the effectiveness of the filter design methods for the real-valued and complex-valued cases, respectively.

Exploring data-driven building energy-efficient design of envelopes based on their quantified impacts

Building performance design plays a key role in reducing the energy consumption of buildings. However, the widely used simulation-based design is facing several challenges, such as the labor-intensive modeling process and the performance gaps between design stage estimations and operational energy use. For these reasons, artificial intelligent methods are expected by designers to improve the efficiency and reliability of building energy-efficient design. To date, there has not been a practical data-driven design method of envelopes. This study aimed at exploring data-driven building energy-efficient design of envelopes based on their quantified impacts. A feature selection method and a game-theoretic method were applied to quantify the impacts of envelopes on space heating and cooling energy, which were performed on two building datasets, one of which is from the U.S. and the other from China. Random forest classifiers were developed to conduct the study. Based on discovered energy patterns and quantified impacts of envelopes on energy consumption, a rectified linear design method of envelopes was proposed with the idea of improving the performance of high-impact envelopes. Besides, a validation study was conducted on two office buildings in the hot-summer cold-winter region. To design the envelopes of a building, the data-driven analysis was driven by its similar buildings other than the whole dataset. Moreover, a detailed energy simulation was conducted to evaluate the energy performance of different design solutions. The results showed that compared with baseline design solutions, new strategies could save 1.05%–21.2% energy for space heating and cooling for these two case buildings. The proposed method is a general building envelope design approach and allows designers to easily find an energy-efficient configuration of envelopes. This study demonstrated the feasibility and effectiveness of the data-driven energy-efficient design of building envelopes.

Alignment Design of Underground Road: A Simulator Study

In order to study the linear combination design method of underground roads, a road model with 16 test sections was designed for 8 common horizontal and vertical line combinations, and two test environments, up and under ground, were built. Fifteen participants participated in the driving simulation experiment. Driving behaviors between different lanes of roads on-ground and underground roads of each test section, each section with up or down slopes and with left or right turns were compared and analyzed. Then the applicability of different horizontal and vertical line combination in underground road design was evaluated.

Experimental dynamic characterization of friction brace dampers and application to the seismic retrofit of RC buildings

Previous earthquakes have caused extensive damage to reinforced concrete (RC) structures with insufficient lateral force resistance or energy dissipation capacity. There is a need to retrofit vulnerable existing RC buildings, particularly those not originally designed for seismic effects or designed to an outdated seismic specification. This study investigates the use of friction dampers as displacement-dependent energy dissipation devices to retrofit RC moment frame structures. First, an experimental program was conducted to characterize the dynamic behavior of friction brace dampers with several different materials, finding that a sintered metal compound provided a stable friction coefficient of 0.4. A strength-based equivalent linearization design procedure was then developed based on the required friction slip force and considering the cracked state of the existing RC structure. A four-story RC school building was then designed using the proposed retrofit design method, validated using nonlinear response history analysis and compared to a previous retrofit scheme that employed buckling-restrained braces (BRBs) and a stiffness-based equivalent linearization design method. The analysis results suggest that the proposed retrofit design method and friction brace dampers are effective in reducing the maximum story drift.

Evaluation of Ground Motion Definition on the Seismic Analysis of Reinforced Concrete Moment Frame Structure

The primary objective of the study is to analyze the effect of the horizontal definition in the ground motion selection, in which, how the target spectra of DBE and MCE resulted from the geometric mean method and NGA West-2 Sa RotD100, the maximum direction method is different from each other. The analysis of the seismic performance of the building is the secondary aim of the research. The linear design methods of equivalent lateral force analysis, response spectrum and seismic response history analysis are performed based on the Myanmar seismic design code to figure out and compare the building responses such as story displacement, story drift, story base shear, and story overturning moment. In this study, the irregular shaped RC building structural responses are also explored with equivalent lateral force analysis (EQLF), response spectrum analysis (RSA) and linear response history analysis (LRHA). The recent ground motion definition response shows great potential in improving the performance-based design of considered structures.

Predicting failure of cracked aluminum plates with one-sided composite patch

Composite patch repairs are an alternative to weld repair methods to arrest crack growth in metal plates. While these repairs have been effective, it has been difficult to use basic linear elastic fracture mechanics (LEFM) theories and design methods based on LEFM to predict the efficacy of patch repairs because the repaired plate exhibits bending and significant crack tip plasticity. In this investigation, we have studied the effect that one-sided low modulus composite patch repairs have on the development of crack tip plasticity on the free surface and through the thickness using large strain area and volume, total axial stress balance, and the free surface J-integral. Digital Image Correlation (DIC) and three-dimensional finite element analysis with first order elements were used to understand the evolution of crack tip plasticity and strain energy release rate to develop a simplified prediction method identifying a characteristic crack opening displacement prior to crack tip behavior of a one-sided composite patch repaired Center-Cracked Tension (CCT) specimen transitioning from Small Scale Yielding (SSY) to Large Scale Yielding (LSY), and eventually the re-initiation of crack growth. This method was then validated by comparing the predicted characteristic transition load to observed ultimate patched CCT specimen load capacity. Results correlated well with predictions when the composite patch was perfectly bonded to the aluminum and predicted characteristic transition loads more than 90 $$\%$$ greater than LEFM based failure predictions and 25 $$\%$$ lower than observed ultimate failure loads, demonstrating the potential to use this method for patch repair optimization.