Optimal pole placement by weight selection

Modern aircraft is designed generally with static unstable configuration in order to achieve the good maneuvering performance and the good controllability. Flight control law design is very important for the modern aircraft. The most importance for the flight control law is sustained flight. This paper presents a method of the state space description static instability mathematic model of modern aircraft. A new flight control law design based on pole placement and state feedback method is given in this paper also. The flight system stability and maneuverability are greatly improved through the method of the pole placement and state feedback. The simulation results show that pole placement method is very important and feasible in modern flight control system design.

This paper presents a method of pole placement in the linear quadratic regulator and its application to the flight control system design. There are three features in the proposed method. First, a weighting matrix that gives desired closed-loop pole locations is obtained by solving a set of differential equations. They are derived from the characteristic equation of the Hamilton matrix. Second, poles can be placed exactly at the desired positions and arbitrarily except the symmetry of complex conjugate poles with respect to the real axis. Third, it is a diagonal weighting matrix that is obtained by the proposed method. The third feature makes output regulation with desired pole locations possible. After demonstrating the effectiveness of the method through a simple literature example, it is then applied to the F-4 aircraft's lateral dynamic model. HE optimal regulator, or linear quadratic regulator (LQR), is a typical state-space design method. It has several features. For example, by imposing penalty on state variables and control inputs in a quadratic performance index, one can investigate tradeoff between system performance and control efforts. Besides, it is well known that the LQR has infinite gain margin and 60-deg phase margin for single-input systems. However, by this technique one cannot assign closed-loop pole locations. Since pole locations have a large effect on time-response characteristics, such as overshoot, rise time, etc., it is desirable to assign pole positions in the LQR design. Pole placement in the LQR is a problem associated with the selection of appropriate weighting matrices, when a set of desired closed-loop eigenvalues (CLEs) are known. This problem has been studied by many researchers since early 1970s, and many papers113 have been published in this research area. Among them, the study of Hayase 1 provides a relation between the weighting matrix and the feedback gains for a single-input system in controllable canonical form. Recently, Ohta et al. 2 showed a simple derivation of the relation. Meanwhile, for multi-input systems, Saif3 established a simple method using aggregation to compute a weighting matrix by which arbitrary and exact pole placement can be attained in a general form. He integrated the previously proposed three approaches.46 All of the aforementioned methods for multi-input systems follow Solheim's approach for placing imaginary parts as well as for placing real parts using the mirror image property.7 Another approach, which is completely different from the preceding approaches, is that of Graupe. In his method, first, differential equations of a weighting matrix with respect to the CLEs are derived, and then a weighting matrix is found as a solution of an optimization problem, wherein the difference between CLEs and assigned eigenvalues is made as small as possible.8 However, it is complicated and does not seem practical. Besides the preceding approaches, there are many approaches such as assigning eigenvalues with prescribed degree of stability, 9 placing eigenvalues into a specified region,10'11 and achieving pole placement asymptotically.12'13 In this paper, we propose a method of pole placement that is very different from the previously proposed methods. Whereas Graupe's differential equations are derived from the Riccati equation, we

Load recovery plays a key role in the safety and performance optimization of mechanical structures, and its accuracy is affected by a variety of factors such as sensor position and direction. Most current sensor optimization methods are based on discrete simulation data, resulting in the optimization quality dependent on the degree of data discretization. This article aims at recovering mechanical structure load using strain response, construct surrogate model to achieve a continuous mapping relationship between the data, and obtain the globally optimal strain gage placement through an optimization method. Firstly, based on the limited simulation data, the comprehensive strain information of the structural surface is obtained by using the spatial strain conversion principle and the local coordinate systems construction method. Secondly, based on the linear superposition relationship between strain response and load, the strain-load coefficient matrix is obtained, and the surrogate model between the strain gage placement and the strain-load coefficient is constructed. Then, the minimization of the variance of the load recovery is taken as the objective function for optimization, and the optimal result is obtained. Finally, both simulation and engineering case studies are carried out. The results verify that the proposed method is capable of accurately recovering the load with an error within 10 –3 %. Moreover, the load recovered at the optimal placement based on the strain response is less susceptible to perturbations. Its corresponding load recovery error is at least 70% lower than that of other placement methods, which indicates a high level of robustness. The proposed method also provides reference and technical support for optimizing strain gage placement on complex surfaces and major equipment.

For a linear time-independent model of spacecraft motion, a method for the optimal pole placement of the spacecraft model transition matrix closed by a feedback is proposed. The method is based on the relationship between the modal and optimization approaches to the synthesis of the feedback ensuring the prescribed quality of the attitude stabilization and stability of the time response of the spacecraft determined by the Kalman-Letov performance index. This relationship is established in the paper. An example of applying the proposed method for controlling the motion of the center of mass and about the center of mass in the stabilization of the program rendezvous trajectory of spacecrafts in the orbital frame of reference is discussed.

The optimal placement method of sensors is carried out based on improved genetic algorithm for solving the sensors optimal placement problem of the health monitoring system for long-span railway bridge. Dual structure coding method is introduced to improve the individual encoding method in the Genetic Algorithm. Adaptive partial matching crossover and inversus mutation method is adopted in the optimal preservation strategy, and the probabilities of crossover and mutation are changed automatically according to the fitness value for obtaining the global optimal solution of the sensor placement. So some defects in other Genetic Algorithm applied in the optimal placement of sensors for major bridge structure, such as slow convergence speed and easily falling into local optimum etc., are overcome, and the convergence is ensured. Then the optimal sensors placement of the health monitoring system for one certain long-span railway steel truss cable-stayed bridge is taken as the example to verify the proposed improved genetic algorithm. The result shows that the proposed method has better global optimization, computational efficiency and reliability in compare with the Simple Genetic Algorithm and General Genetic Algorithm, and can be applied to the actual railway cable-stayed bridge health monitoring system for the optimal sensors placement.

Using a combination of the pole placement and online empirical mode decomposition (EMD) methods, a new algorithm is proposed for adaptive active control of structural vibration. The EMD method is a time-frequency domain analysis method that can be used for nonstationary and nonlinear problems. Combining the EMD method and Hilbert transform, which is called Hilbert–Huang transform, achieves a method that can be implemented to extract instantaneous properties of signals such as structural response dominant instantaneous frequencies. In the proposed algorithm, these estimated instantaneous properties are utilized to improve the pole-placement method as an adaptive active control technique. The required active control gains are obtained using a genetic algorithm scheme, and optimal gains are calculated corresponding to preselected excitation frequencies. An algorithm is also introduced to choose excitation frequencies based on online EMD method resolution. In order to investigate the efficiency of the proposed method, some case studies that include a discrete model, continuous samples of beam and plate structures, and experimental cantilevered beam are carried out, and the results of the proposed method are compared with the preset (nonadaptive) optimal gains conditions.

A New Approach to Optimal Regional Pole Placement

The paper discusses an optimal placement for UPFCs and an optimal method for the selection of global measurements in a wide-area controlled network for the purpose of damping power system oscillations. Both the placement and signal selection methods are optimized to damp interarea oscillations. Optimal UPFC placement is identified by comparing different candidate placements based on the total damping they produce. Optimal selection of output measurements is based on the projection of the right eigenvectors on outputs. After the selection of the desired output measurements, observer gains are designed by LMI approaches. Test results from the IEEE 57 bus test system indicate good potential in terms of selecting UPFC placements and output signals.

The present authors proposed the “quasi-neutral dihedral-effect and directional-stability” (QNDD) airplane, which is a modified neutral dihedral-effect and directional-stability (NDD) airplane for its realization. The QNDD airplane provides a superior tolerance to crosswinds compared to a conventional one by modifying geometric properties: dihedral angle of a main wing and vertical tail volume to achieve small values of and , which results in a small effect of crosswind gust on an airplane’s attitude. While the QNDD airplane yields small and , the NDD airplane yields and equal to zero. When the changes of and due to the wing deformations are considered, the NDD airplane is ideal, while the QNDD airplane is more practical. The QNDD airplane had four real eigenvalues rather than classically two reals and one pair of complex conjugates. The eigenvalues seen in a conventional airplane as a Dutch roll mode were seen to be reals in a QNDD airplane, and the mode was overdamped, which is different from a set of eigenvalues of a conventional one. From the Bode diagrams and unsteady simulations with a discrete gust applied as a crosswind, it was confirmed that the QNDD airplane had a higher tolerance to the crosswind.

At the broken phase of a parity-time (PT)-symmetric dimer where the coupling is weak, the eigenfrequencies are complex conjugate pairs with non-vanishing real parts, leading to oscillation magnitudes with an exponentially growing mode and an exponentially decaying mode. If the large oscillation magnitudes are clamped due to the nonlinear gain of the PT-symmetric dimer, the exponentially growing mode eventually enters the stable oscillations. It was recently demonstrated that such a phenomenon can be utilized for non-reciprocal transmission. The distortion induced by nonlinearity is critical for the non-reciprocal transmission. Here, we experimentally explore the nonlinear distortion in PT-symmetric inductor–capacitor resonators by utilizing discrete components on a printed circuit board. It demonstrates that the IIP3 (the output-referred third-order intercept point) can achieve as high as 38.7 dBm at the frequency of 14.5 MHz corresponding to the maximum forward transmission. The noise figure of the system is measured to be about 11.25 dB.

Multi-component diffusion and penetrative convection

For stable systems, the eigenvalues are complex with a negative real part for underdamped modes. In this case, both the eigenvalues and eigenvectors occur in complex conjugate pairs and Eq. (18) can be expressed in real form by TV terms. In conclusion, this paper points out that the equations of motion of a flexible airplane can be written in the form of a general nonself-adjoint system which can be solved by the eigenfunction expansion.

Deploying shunt capacitor banks in distribution systems can effectively reduce the power loss and provide additional benefits for system operation. In practice, the power loss on distribution transformers can account for a considerable portion of the overall loss. This paper proposes a method for optimal placement of capacitor banks to the distribution transformers to reduce power loss. The capacitor bank locations are considered at the low-side of transformers. The net present value (NPV) criterion is adopted to evaluate the cost benefit of the capacitor installation project. First, an explicit formula for directly calculating the power loss of radial distribution systems is derived. Then, the optimal capacitor bank placement is formulated as a mixed-integer programming (MIP) model maximizing the NPV of the project subject to certain constraints. The model is suitable for being solved by commercial MIP packages, and the operational control of the capacitor banks to maximize the power loss reduction can be simply achieved by local automatic switching according to VAR measurements. The proposed method has been practically applied in the Macau distribution system, and the simulation results show that the proposed method is computationally efficient, and a considerable positive NPV can be obtained from the optimal capacitor bank placement.

Every real polynomial of degree n in one variable with root −1 can be represented as the Schur-Szegő composition of n − 1 polynomials of the form (x + 1) n−1(x + a i ), where the numbers a i are uniquely determined up to permutation. Some a i are real, and the others form complex conjugate pairs. In this note, we show that for each pair (ρ, r), where 0 ⩽ ρ, r ⩽ [n/2], there exists a polynomial with exactly ρ pairs of complex conjugate roots and exactly r complex conjugate pairs in the corresponding set of numbers a i .

Performance-based optimal sensor placement method for single-layer reticulated shells considering modal observability and damage identifiability