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There have been numerous studies on the control of quadcopters. These studies mainly aim to control the flight behavior of quadcopters. To achieve this, researchers have been developing new tools and testing new methods. One of the developed tools is the 3-DOF Hover system, which enables researchers to analyze the flight behaviors of quadcopters, such as roll, pitch, and yaw, even in a physically limited area or only in a computer environment. The control method applied in the control of the 3-DOF Hover system has been determined by the manufacturer as Linear-Quadratic Regulator (LQR). LQR has control parameters that are complex to calculate. This complex calculation process creates an optimization problem. Beyond controlling the 3-DOF Hover system using LQR, this study focuses on calculating the complex control parameters of LQR using optimization algorithms when controlling a dynamic system with LQR. This study includes well-known algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA), as well as an innovative approach known Gray Wolf Optimization (GWO). These algorithms were selected due to their proven effectiveness in various studies. Based on the results obtained from these algorithms, a hybrid algorithm incorporating SA and GWO is proposed. The aim of this hybrid algorithm is to combine the advantages of different methods and achieve a more effective and efficient optimization process. The mentioned hybrid algorithm, obtained by combining SA and GWO, is named hSA-GWO. This hSA-GWO is compared with traditional algorithms, and the comparison results show that the proposed hybrid algorithm can be used as an alternative and competitive method for controlling the flight behaviors of quadcopters. [ABSTRACT FROM AUTHOR]

In this study, a mathematical model of a new hydro-pneumatic damper consists of a double-acting cylinder, two oil chambers, a damping valve, and an accumulator is developed to assess its response to vertical vibrations in a passenger car. The main idea of the new damper aim to make that the damping coefficient in compression differ than that in rebound which achieve more stability specially during cornering. The damping coefficient difference in compression and rebound can be achieved due to the presence of accumulator. Both passive and active hydro-pneumatic suspension systems with the new damper employing different control strategies such as LQR, PID, and H-infinity control, are employed to assess the effectiveness of the suspension system. The investigation focuses on vertical acceleration, pitch acceleration, suspension deflection, and dynamic tire load. The half-car model is simulated using MATLAB/Simulink, and the results for both active and passive hydro-pneumatic suspensions are analyzed in terms of frequency, time, and power spectral density responses. The findings reveal that the active suspension system with H-infinity control demonstrates an 81% improvement in body acceleration and a 92% improvement in pitch acceleration (angular acceleration) compared to the passive hydro-pneumatic suspension which improve the stability of the vehicle during cornering. Similarly, the implementation of LQR-controlled suspension enhances body acceleration and step acceleration by approximately 40% and 57%, respectively, compared to the passive hydro-pneumatic suspension. Moreover, when compared to the passive hydro-pneumatic suspension, the PID-controlled active hydro-pneumatic suspension exhibits a 64% improvement in step acceleration and a 44% improvement in body acceleration.

The rapidly increasing demand for heavy vehicles in the transportation sector has led to more severe road damage and significantly higher road maintenance costs. Investigation of active suspension system incorporating vehicle–road interaction (VRI) can provide effective means to reduce the road damage and improve the ride comfort of vehicles. In this paper, an active vehicle suspension controller based on the strongly stable and robust linear–quadratic regulator (LQR) principle is developed for the time-varying VRI system. The coupled system is modeled by a quarter-car traveling on the road modeled by an Euler–Bernoulli beam resting on a viscoelastic foundation. Two types of road irregularities, deterministic sine wave and random, are considered in the numerical studies. A time-frozen technique, by which the linear time-varying system is converted to a time sequence of time-invariant systems, is applied to solve for the coupled responses. Three variables, the dynamic tire load, vehicle body acceleration, and suspension relative displacement, are used to assess the effectiveness of the LQR-based controller in comparison to the passive suspension system. The performance of the active control is investigated for different vehicle speeds, vehicle loads, and road profiles. Numerical studies show that the controller can effectively reduce the road damage and improve the ride comfort, with a slight increase in the suspension relative displacement. This work lays a useful foundation in the problem formulation and system parameter influences for future vehicle suspension design and road damage mitigation including VRI. [ABSTRACT FROM AUTHOR]

In-wheel motor vehicles are gaining attention as a new type of electric vehicle due to their efficient power units located inside each wheel hub. However, they are more susceptible to wheel resonance due to the increase in unsprung mass caused by the weight of the motor. This can result in both decreased ride comfort and driving stability. To resolve this issue, in this study, we aim to apply an optimal switching controller with a semi-active actuator—a magnetorheological (MR) damper. For the implementation of the optimal switching controller, road type classification is also carried out. An acceleration sensor is used for the road type classification, and the control logics include a ride comfort controller (the linear quadratic regulator (LQR_Paved Road)) and a wheel motion controller (LQR_Off Road) for improved driving stability. For paved roads, the LQR_Paved Road control input is applied to the MR damper. However, if a road type prone to wheel resonance is detected, the control logic switches to the LQR_Off Road. During the transition, a weighted average of both the LQR_Paved Road and LQR_Off Road control input is applied to the actuator. Computer simulations are performed to evaluate the vibration control performance, including the ride comfort and driving stability on various road profiles. [ABSTRACT FROM AUTHOR]

In our study, we compared classical genetic algorithm (GA) and non-dominated sorting GA (NSGA) II to optimize LQR and sliding mode control (SMC) for an inverted pendulum. We aimed to identify the algorithm that best improves stability and peak performance. Our results clarified each algorithm’s unique strengths. The provement is shown in Matlab simulations.

This paper surveys the Linear Quadratic Estimation (LQE) and Model Predictive Control (MPC) discrete control methods applied to the Acrobot system. Both techniques aim to achieve and maintain a balanced position for the Acrobot. Through evaluation and comparison, we highlight their strengths, limitations, and potential applications, offering insights for future robotic control research.

Ball and plate system (BPS) is known as a nonlinear multi-input multi-output (MIMO) system that has been usually used to investigate and develop control algorithms. In this paper the study deals with a 3-RRS parallel manipulator which has a metal ball, three DC motors with linkage mechanism to a fixed base that can be a resistive touch screen . The moving base has two rotational movements, it can be rotated around the x-axis and y-axis and translated along the z-axis. The main purpose of this study is obtaining dynamics equations of motions and designing PD and LQR controllers. Through simulation and experiment, both control algorithms are proved to work well on this model.

In this paper, we apply genetic algorithm (GA) to optimize LQR controller – a linear control algorithm which stability is guaranteed by mathematics. This searching algorithm proves its ability in finding better control parameters through generations. Our model is ball and beam (B&B) – a classical single input – multi output (SIMO) system. This system is balanced around equilibrium point in simulation.

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Flapping wings provide a theoretically energy efficient mode of lift and maneuverability in Unmanned Air Vehicles (UAVs) for a wide variety of applications. However, their performance is significantly degraded in presence of turbulence. In order to address this problem of turbulence, motivated by the covert feathers present in birds, this paper presents a multibody Bond Graph Model (BGM) of a biologically inspired Flapping Wing UAV (FUAV) capable of flight in turbulent airflows. To further simplify computations and carry out stability analyses, Reduced Order Modeling (ROM) of the multibody model is offered. For the proposed multibody FUAV, a biomimetic closed loop Linear Quadratic Regulator (LQR) based flight controller is created in order to achieve stable flight during gusts. A successful gust mitigation of up to 32% is shown in simulations of the optimized model and proposed control approach, which consistently show stable behavior under turbulent flight. Furthermore, the accuracy and effectiveness of the suggested control approach is confirmed by the strong agreement between previously published experimental data and the present findings. [ABSTRACT FROM AUTHOR]

In order to further improve the control effect of proportion integral differential (PID) control and linear quadratic regulator (LQC) control, and improve vehicle ride comfort and enhance body stability, the 7 DOF semi-active suspension model was established, and the fractional order PIλDμ-LQR controller was designed by combining fractional order PIλDμ control theory and LQR control theory. The semi-active suspension model in this paper is more complex, and there are many parameters in the controller. The optimal weighting coefficient of 12 vehicle smoothness evaluation indicators and parameters Kp, Ki, Kd, λ and μ in the controller were founded by NSGA-II algorithm. After optimization, the optimized parameters were brought into the controller for random pavement simulation. Compared to the traditional passive suspension, fractional order PIλDμ individual control and LQR separate control, the simulation results show that the effect of fractional order PIλDμ-LQR control is very significant. The evaluation index of vehicle smoothness has been significantly improved, and the use of fractional order PIλDμ-LQR control has significantly improved the working performance of the suspension and improved the smoothness of the vehicle. At the same time, the adjusting force output of the actuator is very balanced, which inhibits the roll of the body and improves the anti-roll performance. After simulation, the excellent performance of the designed fractional PIλDμ-LQR controller was verified, and the introduced NSGA-II algorithm played an important role in the controller parameter tuning work, which shows that the fractional order PIλDμ-LQR controller and NSGA-II algorithm cooperate with each other to achieve good control effects. [ABSTRACT FROM AUTHOR]

Manuscript provides a key technology, namely Input-Output Feedback Linearization Associates with Linear Quadratic Regulator (for short, IOFLALQR). The objective of this research is to study the possibility of integrating two control strategies, which includes input-output feedback linearization technique (for short, IOFL) and linear quadratic regulator controller (for short, LQR), for stabilization control of Furuta pendulum system. Furuta pendulum system belongs to the group of under-actuated robot systems. In this work, structure of IOFLALQR, control implementation, comparison of IOFLALQR and conventional LQR are adequately studied and discussed. Simulation is completed in MATLAB/Simulink environment and experiment is done on real-time experimental setup. Numerical simulation and experimental results show that the IOFLALQR are implemented on Furuta pendulum successfully. Besides, results have been drawn for demonstrating IOFLALQR better than another classical method.

This paper proposes an adaptive control technique (ACT) for a three-phase, three-level, T-type rectifier based on online disturbance estimation and compensation. The proposed solution also regulates the DC-link voltage and grid currents under uncertainties, disturbances, measurement noises, and unbalanced grid voltages without cascaded control. The proposed controller consists of two layers; the first one is responsible for estimating nonlinearities and model uncertainties based on Kalman Filter Algorithm (KFA). The second layer is responsible for controlling both grid currents and DC link voltage using Linear Quadratic Regulator (LQR). The proposed controller is analyzed theoretically, validated experimentally, and the performance of the proposed controller is compared with two other controllers. The simulation and experimental results prove the superiority of the proposed controller and show that the proposed controller can ensure fast-tracking performance with almost zero steady-state error. The proposed controller has the ability to overcome severe disturbances such as AC and DC side disturbances, measurement noises, and mathematical model’s uncertainties even up to 400%.

In-wheel motor vehicles are gaining attention as a new type of electric vehicle due to their efficient power units located inside each wheel hub. However, they are more susceptible to wheel resonance due to the increase in unsprung mass caused by the weight of the motor. This can result in both decreased ride comfort and driving stability. To resolve this issue, in this study, we aim to apply an optimal switching controller with a semi-active actuator—a magnetorheological (MR) damper. For the implementation of the optimal switching controller, road type classification is also carried out. An acceleration sensor is used for the road type classification, and the control logics include a ride comfort controller (the linear quadratic regulator (LQR_Paved Road)) and a wheel motion controller (LQR_Off Road) for improved driving stability. For paved roads, the LQR_Paved Road control input is applied to the MR damper. However, if a road type prone to wheel resonance is detected, the control logic switches to the LQR_Off Road. During the transition, a weighted average of both the LQR_Paved Road and LQR_Off Road control input is applied to the actuator. Computer simulations are performed to evaluate the vibration control performance, including the ride comfort and driving stability on various road profiles.

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Dokuz Eylul University Muhendislik Faculty of Engineering Journal of Science & Engineering / Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi is the property of Dokuz Eylul Universitesi Muhendislik Fakultesi Fen ve Muhendislik Dergisi and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The present work proposes the use of a hybrid controller combining concepts of a PID controller with LQR and a feedforward gain to control the positioning of a 2 DOF robotic arm with flexible joints subject to non-ideal excitations. To characterize the performance of the controls, two cases were studied. The first case considered the positioning control of the two links in fixed positions, while the second case considered the situation in which the second link is in rotational movement and the first one stays in a fixed position, representing a system with a non-ideal excitation source. In addition to the second case, the sensitivity of the proposed controls for changes in the length and mass of the second link in the rotational movement was analyzed. The results of the simulations showed the effectiveness of the controls, demonstrating that the PID control combined with feedforward gain provides the lowest error for both cases studied; however, it is sensitive to variations in the mass of the second link, in the case of rotational movements. The numerical results also revealed the effectiveness of the PD control obtained by LQR, presenting results similar to the PID control combined with feedforward gain, demonstrating the importance of the optimal control design. [ABSTRACT FROM AUTHOR]

The choice of a mathematical model of eye movement has had a significant impact on scientific research. This research resulted in a controlling robotic arm that could follow the movement of the human eye and thoroughly examine the structure of the human eye. Exploring the previous models, a model equivalent to a robot with two degrees of freedom is presented. Then, by designing and simulating an optimal linear square controller on the desired system, we could model an eye robot. The purpose of tracking is to target the system, which is shown by simulating this controller. This paper describes how to design a fuzzy controller for the system by presenting the simulation results. Finally, the performance of the two control methods in non-zero initial conditions, rapid eye movements, and uncertainty in the model system constructions are compared. The simulation results show that despite the system control provided by both control methods, the fuzzy control method has a better performance for tracking fast eye movements. This method is resistant to modeling uncertainties by using the qualitative behavior of the system instead of its exact mathematical model. Also, the smaller volume of simulation of control inputs in the fuzzy controller will significantly reduce costs by using this controller.

Today, we are witnessing an increasing trend in the number of soft pneumatic actuator solutions in industrial environments, especially due to their human-safe interaction capabilities. An interesting solution in this frame is a vacuum pneumatic muscle actuator (PMA) with a bellow structure, which is characterized by a high contraction ratio and the ability to generate high forces considering its relatively small dimensions. Moreover, such a solution is generally very cost-effective since can be developed by using easily accessible, off-the-shelf components combined with additive manufacturing procedures. The presented research analyzes the precision positioning performances of a newly developed cost-effective bellow PMA in a closed-loop setting, by utilizing a Proportional-Integral-Derivative (PID) controller and a Linear Quadratic Regulator (LQR). In a first instance, the system identification was performed and a numerical model of the PMA was developed. It was experimentally shown that the actuator is characterized by nonlinear dynamical behavior. Based on the numerical model, a PID controller was developed as a benchmark. In the next phase, an LQR that involves a nonlinear pregain term was built. The point-to-point positioning experimental results showed that both controllers allow fast responses without overshoot within the whole working range. On the other hand, it was discovered that the LQR with the corresponding nonlinear pregain term allows an error of a few tens of micrometers to be achieved across the entire working range of the muscle. Additionally, two different experimental pneumatic solutions for indirect and direct vacuum control were analyzed with the aim of investigating the PMA response time and comparing their energy consumption. This research contributes to the future development of the pneumatically driven mechatronics systems used for precise position control. [ABSTRACT FROM AUTHOR]

This paper aims to derive a dynamic model of ball and beam systems (BBS), design, and implement the optimal controller linear quadratic regulator (LQR) with cascaded feedback linearization controller (FLC). It is known that missing information of the parameter of the system model can cause undesired tracking results. The LQR-FLC can solve the tracking problem caused by model uncertainty. The LQR controller, the inner-loop controller, is designed based on the derived BBS dynamics model. Then FLC, the outer-loop controller, is designed to get the desired tracking error dynamics. By using LQR-FLC, one can use the simple PD controller to design the tracking error dynamics. In addition, the estimator is designed to provide the controller with the full-states information. This research is worth investigating because the LQR-FLC scheme for controlling the BBS is missing in the literature. The experiment is carried out using a hardware in loop (HIL) scheme where MATLAB-Simulink is connected to a microcontroller. Simulation and experimental results show the effectiveness of the proposed cascaded LQR-FLC. [ABSTRACT FROM AUTHOR]

The vibration control for building structures using hybrid control (base isolators BI and Active Tuned Mass Dampers-ATMDs) has attracted the attention of researchers. This paper establishes a hybrid vibration control system of structure and compares structural response and active tuned mass damper performance among the structure using two different control algorithms (PID and LQR). Through simulation research, from the comparative analysis of performance indexes of structural response and ATMD performance, it is concluded that the LQR controller outperforms the PID controller in reducing the structural responses.

We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find strategies which are successful as the time horizon tends to infinity, our strategy achieves lowest expected cost up to a constant factor for a fixed time horizon. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a wavelet‐based strategy for fore‐aft vibration control of onshore horizontal axis wind turbine tower. For this purpose, an active tuned mass damper is combined with an aero‐servo‐elastic turbine model in the multi‐body framework. The combined system is exposed to turbulent wind and seismic ground motion to investigate the controller performance in extreme operating conditions. The optimal tuning is achieved by frequency‐dependent gain scheduling via wavelet transform. Analytic Morse wavelet is used as a basis function for transforming the input and feedback to recast the classical linear quadratic regulator (LQR) in the time‐frequency domain over a finite time horizon. The scale‐dependent differential Riccati equations are solved for optimal gains, which are used to estimate the optimal control force. Numerical studies presented in this paper demonstrate the advantage of the proposed gain scheduling over classical LQR. The efficiency of the proposed algorithm is verified using different flow conditions and seismic input, where the performance is compared with benchmark results. [ABSTRACT FROM AUTHOR]

Gait disorders, muscle weakness, spinal cord injuries (SCIs) and other work-related disorders have increased the need for rehabilitation exoskeletons—specifically, for the hip because a huge percentage of mechanical power comes from the hip joint. However, realising a lightweight rehabilitation hip exoskeleton for mobility and at-home use with reliable control is challenging. The devices developed are restricted by a joint actuator and energy source design and tend to have various uncertainties. Thus, this study tested the robustness of four optimal controller cases in a simulation-based environment. We sought to determine whether the most robust optimal controller consumed less energy and demonstrated better performance in tracking the desired signal. The robustness of the optimal cases was tested with the hip torque signals of healthy subjects. The number of sit-to-stand (STS) instances and the walking distance at various speeds were calculated. The results showed that the most robust case controller was more energy efficient for STS, but not for walking activity. Furthermore, this study provides compelling evidence that various optimal controllers have different degrees of robustness and effects on energy consumption. [ABSTRACT FROM AUTHOR]

The choice of a mathematical model of eye movement has had a significant impact on scientific research. This research resulted in a controlling robotic arm that could follow the movement of the human eye and thoroughly examine the structure of the human eye. Exploring the previous models, a model equivalent to a robot with two degrees of freedom is presented. Then, by designing and simulating an optimal linear square controller on the desired system, we could model an eye robot. The purpose of tracking is to target the system, which is shown by simulating this controller. This paper describes how to design a fuzzy controller for the system by presenting the simulation results. Finally, the performance of the two control methods in non-zero initial conditions, rapid eye movements, and uncertainty in the model system constructions are compared. The simulation results show that despite the system control provided by both control methods, the fuzzy control method has a better performance for tracking fast eye movements. This method is resistant to modeling uncertainties by using the qualitative behavior of the system instead of its exact mathematical model. Also, the smaller volume of simulation of control inputs in the fuzzy controller will significantly reduce costs by using this controller. [ABSTRACT FROM AUTHOR]

Automotive suspension is a mechanical device used in automobiles to attenuate vibrations, which are caused by the undulation of the floor. This device can be modeled by a mass-spring-damper system, and the damper used in most real situations is a viscous medium damper, which dissipates energy passively. In this work, a 1=4 model of automotive suspension was analyzed when the passive shock absorber is exchanged for a magnetorheological shock absorber, whose control current is determined by a law of Optimal Linear Control. Based on the analyzes made in terms of displacement and acceleration, more satisfactory results were obtained in the system containing the AMR, in contrast to the results obtained with the presence of the passive damper. [ABSTRACT FROM AUTHOR]

The seismic performance of nonstructural elements is crucial for buildings to remain functional during and after earthquakes. Since the seismic damage to many nonstructural elements is sensitive to their acceleration and/or velocity responses, dynamic testing becomes inevitable in assessing their seismic performance. We propose a novel experimental method that enables the dynamic testing of various layouts of nonstructural elements through a passively controlled and adaptable testbed mounted on and driven by a shake table. The testbed is made of three consecutive floors of steel structure. The bottom two floors provide a space to accommodate a full-scale room. The third floor on top adds additional degrees of freedom for the ease of tuning the dynamic properties of the testbed. The input motion of the shake table is generated by an offline control algorithm to drive the testbed so that its bottom two floors trace the time histories of target floor motions of the building of interest. This paper introduces the key aspects of the new method, including the derivation of the desired structural properties of the testbed, and the control algorithm that generates the necessary input motion of the shake table. An example of simulating the motions of two consecutive floors in the middle of a 42-story tall building is adopted to assist illustrating and validating the method by numerical simulation and experimental demonstration. [ABSTRACT FROM AUTHOR]

The underframe passive inerter-based suspended device, based on the inerter-spring-damper vibration attenuation structure, could improve the dynamic performance of the train body, but its parameters are fixed and cannot meet the dynamic performance requirements under different operating conditions. Therefore, a semi-active inerter-based suspended device based on the linear quadratic regulator (LQR) control strategy is proposed to further enhance the dynamic performance. The rigid-flexible coupling vertical dynamic model of the train body and an underframe semi-active inerter-based suspended device are established. The structural parameters of the semi-active inerter-based suspended device are adjusted using LQR control strategy. Dynamic response of the system is obtained using the virtual excitation method. The dynamic characteristic of the system is evaluated using the Sperling index and compared with those of the passive and semi-active traditional suspended devices as well as the passive inerter-based suspended devices. The vertical vibration acceleration of the train body and Sperling index using the semi-active inerter-based suspended device is the smallest among the four suspended devices, which denotes the advantages of using the inerter and LQR control strategy. The semi-active inerter-based suspended device could decrease the vertical vibration acceleration of the train body and further suppress its elastic vibration in the lower frequency band, more effectively than the other three suspended devices. Overall, the semi-active inerter-based suspended device could significantly reduce elastic vibration of the train body and improve its dynamical performance. [ABSTRACT FROM AUTHOR]

The size of unmanned aerial vehicles (UAVs) makes them very sensitive to atmospheric turbulences thereby restraining their capability of stable flight. To resolve this serious concern, disturbance mitigation capabilities of birds have been studied in depth and it has been found that birds use covert feathers to alleviate gusts. This paper proposes a model of bio-inspired gust mitigation system (GMS) for a flapping wing UAV (FUAV) imitating covert feathers using bond graph modeling approach. Further, reduced order modeling of the GMS is presented for reducing the computational complexity and performing the stability analysis. A biomimetic closed loop flight controller based on LQR is developed for the proposed GMS to achieve stable flight during gusts. Finally, simulations of the optimized model and proposed control strategy always depict stable behavior during turbulent flight with successful gust mitigation up to 50%. Moreover, close agreement between present results and experimental data in literature validates the proposed control method. [ABSTRACT FROM AUTHOR]

Copyright of Maritime Faculty Journal (Dokuz Eylül University) is the property of Dokuz Eylul University Maritime Faculty Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This brief proposes a generalization of the linearization technique in which the computation of the Jacobian matrices at the state trajectory of interest is replaced by the multiple integral over the state and input spaces of the Jacobian matrix functions multiplied by a weighting function. The standard linearization can be recovered as a particular case of the proposed weighted linearization by choosing the weighting function as an appropriately shifted multivariable Dirac delta function. Linear-quadratic regulator (LQR) design is used in the illustrative examples to show the potentiality of the proposed technique. [ABSTRACT FROM AUTHOR]

The paper deals with the development of the finite element method (FEM) model of piezoelectric beam elements, where the piezoelectric layers are located on the outer surfaces of the beam core, which is made of functionally graded material. The created FEM model of piezoelectric beam structure is reduced using the modal truncation method, which is one of model order reduction (MOR) method. The results obtain from reduced state-space model are compared with results obtain from finite element model. MOR state-space model is also used in the design of the linear quadratic regulator (LQR). Created reduced state-space model with feedback with the LQR controller is analysed and compared with the results from FEM model.