76 results about "Linear matrix" patented technology

The invention discloses a lightweight block cipher binary linear matrix automatic design method and system. Meanwhile, the implementation cost and the safety property of constructing the binary linear matrix are considered, and from the perspective of circuit implementation, an automatic tool is used for constructing the binary linear matrix. From the perspective of circuit realization, the realization cost of two dimensions of area and time delay can be considered, and the cryptography cost is constrained while the security property of the binary linear matrix is considered. In addition, a g-XOR method is used for designing the matrix, and compared with a traditional method for iteratively designing according to the structure or constructing a binary linear matrix through mathematical derivation, the implementation cost is the lowest, all solutions for constructing the binary linear matrix can be included, and the method can be used for judging the cost limit.

The invention belongs to the technical field of lower limb rehabilitation, and discloses a man-machine coupling system intelligent cooperative control method and device based on deterministic learning. Establishing a state-space equation of the lower limb exoskeleton robot, defining a tracking error, and designing a self-adaptive neural network controller of the lower limb exoskeleton robot; defining an expected position state vector and a real position state vector of the walking robot, solving a position state vector error, and designing a self-adaptive neural network controller of the walking robot; the method comprises the following steps: constructing a time-varying linear matrix, verifying the exponential stable convergence characteristic of the time-varying linear matrix under a continuous excitation condition on the basis of an adaptive neural network controller, storing nonlinear dynamic knowledge of a man-machine coupling system, and constructing a learning controller by using the learned knowledge. According to the method, while the unknown dynamic state of the man-machine coupling system is accurately modeled, the continuous excitation condition is ensured, so that accurate and stable trajectory tracking control is realized.

The invention discloses a soft package battery fault detection method and system based on an adaptive neural network, and the method comprises the steps: constructing a battery temperature spatial distribution model considering thermal anomaly and sensor faults, carrying out the homogenization of non-homogeneous boundary conditions through employing an auxiliary function decomposition method, and building an ODE dimension reduction system in combination with a Galerkin method; the method comprises the following steps: acquiring surface temperature, current and terminal voltage data of a battery, designing stable parameters through a linear matrix inequality, estimating a nonlinear thermal generation item by adopting a neural network observer with a self-adaptive weight matrix, and constructing an error system; a lumped residual error evaluation mechanism is introduced, a dynamic fault threshold value is generated based on a kernel density estimation technology, and online detection is completed by comparing a residual error evaluation value of an output estimation error with the threshold value in real time. According to the method, limitation of a traditional lumped parameter model is broken through, distributed thermal fault detection of the two-dimensional soft package battery can be achieved only through a small number of thermocouples, the hardware cost is greatly reduced while precision is guaranteed, and a new technical path is provided for power battery safety management.

The invention provides a multi-cylinder synchronous accurate control method for a hydraulic jacking system of a tower crane, and belongs to the technical field of tower cranes. A pressure sensor and a displacement sensor are mounted on each hydraulic cylinder of a hydraulic jacking system of the tower crane, and a force sensor is arranged at a key position of a tower body, so that a multi-parameter real-time monitoring network is established; an improved Gaussian kernel function nonlinear matrix mapping algorithm is adopted to calculate a pressure deviation coefficient and a displacement synchronization metric value between hydraulic cylinders, the pressure adjustment processing frequency is dynamically adjusted according to the pressure deviation coefficient value, and self-adaptive load balancing control is achieved through tower body stress unbalance threshold value calculation and stress adjustment gain calculation. And finally, the flow distribution of each hydraulic cylinder is adjusted through a proportional valve, and the convergence of the system is ensured by utilizing Lyapunov stability analysis, so that the technical problem that the multi-cylinder synchronous control of the hydraulic jacking system of the tower crane is not accurate enough is solved.

The invention relates to the technical field of network acceleration, and discloses an edge-end large language model reasoning acceleration method and accelerator, and the method comprises the following steps: reconstructing a calculation process of a decoding stage, and carrying out the deep fusion of a multi-head attention mechanism and the calculation operation of a feedforward network; the weight and key value data are stored in HBM, and the coefficient and the accumulated attention score are stored in DDR; for linear matrix calculation, a unified matrix calculation unit is used for executing multi-precision matrix operation; for nonlinear function calculation, a mathematical transformation and linear fitting method is adopted, a Softmax function is converted into operation with 2 as the bottom through a bottom conversion formula, and truncation and third-order linear fitting are conducted on a Sigmoid function; and constructing a key value screening algorithm based on the accumulated attention score, dynamically adjusting a key value storage position, maintaining a recent key value cache region and an important key value cache region in a limited cache space, and realizing key value efficient cache in long text reasoning.

The invention provides an optical neural network computing system and method based on time domain excitation characteristics, and the system comprises a pulse clock sequence module which is used for generating a reference time sequence; the multi-channel pulse laser array is used for generating semiconductor neuron laser pulses with subnanosecond pulse width based on a reference time sequence; the time domain and wavelength division multiplexing module is used for simultaneously performing time domain coding and wavelength division multiplexing on the laser pulse based on a reference time sequence to generate a first optical signal; the reconfigurable weight matrix module is used for performing all-optical linear matrix operation and weight mapping on the first optical signal to obtain a second optical signal; the neuron activation module is used for performing nonlinear activation processing on the second optical signal based on an LIF theory to obtain an activated optical signal; and the output module is used for carrying out decoding and photoelectric conversion on the activated optical signal to obtain a network reasoning result.

The application discloses an optoelectronic computer based on time domain all-optical signal serial-parallel hybrid computing, which is composed of an electrical transceiving module, a light source module, a linear matrix vector computing module, a summation separation module and a nonlinear activation module.The application adopts time sequence encoding serial input, and multiple input signals are simultaneously and parallelly calculated, so that all computing steps of a full connection neural network, i.e., linear calculation, summation operation and nonlinear activation, can be completed in the optical domain, and the host end only needs to send input data and receive the final computing result.The application has the following advantages compared with other comparative applications: multiple matrix-vector multiplication operation can be completed in parallel; only one optical element is used to complete summation and nonlinear activation operation on multiple multiplication vectors, thereby reducing the hardware deployment pressure; and the bandwidth loss of a pure serial time domain computing method is relieved through serial-parallel hybrid encoding in the time domain, and the computer computing speed is improved.

The invention discloses a load frequency coordination optimization control method, and belongs to the technical field of power system load frequency control technologies. The method comprises the following steps: obtaining a frequency response state space model of a hybrid energy storage-containing two-region interconnected power system through mechanism analysis, performing discretization processing, converting the model into a discretization model, and further establishing a discretization prediction model of the system; analyzing constraints existing in the system, and converting the constraints into a linear matrix inequality; and finally, establishing an objective function of the system, performing online rolling optimization on the control quantity, and designing a multi-region controller, thereby realizing a load frequency coordination optimization control effect of the interconnected power system containing hybrid energy storage. The problems of insufficient flexible resources and poor adjusting characteristics of frequency modulation of an electric power system are solved, coordination and cooperation of battery energy storage, pumped storage and a traditional thermal power generating unit are achieved through coordination control, the frequency response performance of the system is improved, the nonlinear constraint problem existing in the system is solved, and potential safety hazards caused by overload work of equipment are avoided.

The invention discloses an approximate iteration analytic calculation method for a flight trajectory of a hypersonic flight vehicle, which comprises the following steps of: firstly, establishing a gliding flight dynamics mode of the hypersonic flight vehicle, and ignoring lateral motion to obtain a longitudinal plane dynamics model in a linear matrix differential equation form; secondly, according to the characteristics of different types of flight trajectories, performing targeted simplification on a linear matrix differential equation, and analyzing the characteristics of a jump gliding trajectory and a balanced gliding trajectory through matrix eigenvalues; then, on the basis of the quasi-equilibrium gliding condition, lift-drag ratio characteristics of the equilibrium gliding track are analyzed; then, an approximate dynamic model in a short-time period is established, and a flight path analytical expression in the short-time period is obtained; and finally, based on the flight path analytical calculation expression in the short-time period, proposing a flight path approximate iteration analytical calculation process in the long-time period. The method is simple in structure and easy for engineering realization, and has a relatively large popularization and application space.

The application provides a power system transient stability evaluation method and a power system operation trajectory prediction method based on a Koopman operator, the power system transient stability evaluation method comprising the following steps: S1, collecting operation trajectory data of state variables of a power system; S2, using an EDMD method to increase dimensions of the collected state variables to a high-dimensional linear space to approximate an action of the Koopman operator by using a limited-dimensional linear matrix K ; S3, using spectral decomposition of the Koopman operator to locate discrete spectra of stable equilibrium points of the power system, and using characteristics of eigenvalues of the Koopman operator and inverse mapping of dictionary functions to find stable equilibrium points of the power system in an original state space; and S4, based on the obtained stable equilibrium points and analysis of a stable mechanism of a linear system, constructing a power system transient stability criterion, and using the transient stability criterion to judge whether the system is transiently stable after the power system suffers from a large disturbance and collects an arbitrary working point.

The invention relates to a matrix type differential passivity index determination method and device, equipment and a storage medium. The method comprises the following steps: acquiring a linear system model corresponding to target equipment in a power system, wherein the power system is a multiple-input multiple-output system; determining a corresponding differential passivity equivalent system model according to the linear system model; based on the linear matrix inequality, a matrix type passivity index of the differential passivity equivalent system model is solved, the matrix type passivity index is used as a matrix type differential passivity index of the linear system model, the matrix type differential passivity index is in a matrix form, and the matrix type differential passivity index is used as a differential passivity index of the linear system model; matrix elements in the ith row and the jth column in the matrix represent coupling passivity characteristics between an input channel i and an output channel j in the power system. By adopting the method, the passivity characteristics in the MIMO dynamic system can be represented more accurately and comprehensively.

The invention relates to the technical field of earphone noise reduction methods, in particular to a collaborative optimization method for earphone hybrid active-passive noise reduction, which comprises the following steps: firstly, constructing a passive acoustic unit database; secondly, establishing a transfer function neural network model of the passive acoustic unit based on the database; thirdly, constructing a multi-objective optimization problem of the passive acoustic unit structure; then, constructing a hybrid active and passive noise reduction system; and finally, based on the constructed linear matrix model, targets inside and outside the noise frequency band in the hybrid noise reduction system are determined, multi-target collaborative optimization is completed, and respective advantages of active noise reduction and passive noise reduction are fully exerted. The optimization of the passive noise reduction structure improves the sound insulation effect of middle and high frequency bands, and makes up for the deficiency of active noise reduction in the frequency band; the optimization of the active noise reduction algorithm further enhances the noise reduction effect of the low-frequency band, and the active noise reduction algorithm and the low-frequency band form good complementation; through collaborative optimization, the overall noise reduction performance is far better than the effect of a single technology.

The invention belongs to the technical field of communication privacy protection, and particularly relates to a multi-user downlink robust beam forming method based on a differential privacy mechanism. The method comprises the following steps of: estimating a downlink channel vector by a user; the user adds differential privacy noise into the channel vector and feeds back the difference privacy noise to the base station; the base station enables the transmitting power to be minimized under the constraint of a signal to interference plus noise ratio according to the disturbed channel vector modeling optimization problem; using a positive semidefinite relaxation method to convert an optimization problem; using an S-process method to convert the non-convex constraint into a linear matrix inequality; solving a positive semidefinite programming problem by using a CVX optimizer; and restoring the rank-one constraint to obtain an optimal beam forming vector. According to the invention, the location privacy of the user can be effectively protected from being leaked; and on the premise that the requirement of the communication signal to interference plus noise ratio is met, the transmitting power is minimized, excellent system performance is kept, and good robustness and practical value are achieved.

The invention discloses a linear matrix neural network computing chip construction method based on a Mach-Zehnder interferometer, relates to the technical field of microelectronics, and has the technical key points that the feasibility of a coherent optical neural network architecture is confirmed by performing cascade topological connection on a silicon-based MZI rectangular array; the design of a real number matrix photon calculation architecture is realized, and corresponding test processes and experience are provided for subsequent work.

The invention provides an environment adaptive formation control method based on a free parameterization stabilization network, and the method comprises the steps: automatically switching between a compact formation and a standard formation according to the real-time distance from the geometric center of the formation to an obstacle, and achieving the intelligent reconstruction of a formation shape through a preset distance threshold value and a smooth transition mechanism; a free parameterized stable network architecture is adopted to realize parameterized dynamic operator design of each spatial distributed control unit, and distributed information exchange is realized through a sparse interconnection topology isomorphic with a spatial system communication graph; a controller parameter unconstrained scheme suitable for a space environment is constructed by utilizing the inherent stability property of a free parameterized stable network structure, so that the stability of a space closed-loop system can be ensured for any parameter value, the feasibility constraint of a linear matrix inequality is avoided, and unconstrained gradient learning of a three-dimensional distributed controller is realized.

The invention discloses a finite element multi-physical field simulation-oriented metal thin layer boundary condition modeling method, which is used for carrying out rapid equivalent modeling on a rich structure of a metal thin layer in finite element electromagnetic-thermal-force multi-physical calculation so as to achieve the purpose of reducing the calculation complexity. In complex microwave integrated devices, circuits and microsystems, multi-scale metal and thin-layer structures are rich, when a traditional finite element is adopted to carry out multi-physics field numerical solution, volume grids are generally needed to be generated for all materials, the generation of the volume grids of the thin-layer metal can remarkably increase the number of the grids, meanwhile, the mass of grid units is reduced, and the number of the grid units is reduced. And the solving complexity of the linear matrix system is further improved. According to the modeling method disclosed by the invention, the thin metal structure is regarded as planarization, so that the modeling calculation complexity is greatly simplified. Specifically, a large-scale frequency domain electromagnetic system can be efficiently solved in parallel by introducing tangential gradient components of equivalent heat flux and stress to replace a metal thin layer result and adopting a domain decomposition (DDM) method.

To speed up image processing by reducing tokens to be calculated in ViT (VisionTransformer).SOLUTION: Extracting, from a first input feature amount input at a first time point, a changed portion that has changed from a second output feature amount output at a second time point prior to the first time point; And a sparse MSA (Multi-HeadSelf-Attention) processing unit including an extraction unit that generates a change matrix based on a change portion of a first matrix indicating a first input feature amount, a Linear processing unit that calculates a Linear matrix which is a matrix product of the change matrix and a weight matrix, and a replacement unit that replaces a portion corresponding to a change portion of a second matrix indicating a second output feature amount with the Linear matrix calculated by the Linear processing.SELECTED DRAWING: Figure 1

The invention provides a static output feedback dynamic decoupling control method for an unmanned surface vehicle, and belongs to the technical field of motion control and intelligent decision of the unmanned surface vehicle. Comprising the following steps: modeling a motion control system of the unmanned surface vehicle into a discrete time linear system model; a zero block is added into a matrix related to control input, a real matrix is correspondingly introduced into control gain, and a closed-loop system is augmented, so that an additional degree of freedom is introduced for a proposed comprehensive condition. On the basis of the provided multiple Lyapunov functions, the functions are formed by the sum of the Lyapunov functions depending on the system states at different moments, and sufficient conditions represented by linear matrix inequality are deduced to ensure the stability and expected performance of the closed-loop system. Compared with an existing method, decoupling can be achieved without a specific structure of a correlation matrix, and a better result can be obtained.

The invention provides a pixel channel adjustment method and device, equipment and a storage medium. The method comprises the following steps: acquiring a plurality of channels of a pixel point; each channel is provided with an initial value; for an initial numerical value, processing the initial numerical value based on a linear matrix to obtain a calculation numerical value; detecting the calculation value based on a first preset adjustment algorithm, and if the calculation value is smaller than a first preset threshold value, adjusting the calculation value based on a first preset curve to obtain a first intermediate value; the first intermediate value is larger than or equal to a first preset threshold value and smaller than or equal to a second preset threshold value; detecting the calculated value based on a second preset adjustment algorithm, and if the calculated value is greater than a second preset threshold, adjusting the calculated value based on a second preset curve to obtain a second intermediate value; and obtaining a target value based on the first intermediate value and the second intermediate value. According to the technical scheme of the invention, the editing can be prevented from exceeding the numerical value represented by the standard, so that the shadow details and highlight details of the image are reserved.

The invention discloses an anti-DoS attack and actuator saturation power system memory event trigger insurance cost control method and system, and relates to the technical field of network control systems. Establishing a state-space equation based on the dynamic characteristics of the power system; key influence factors in operation of the power system and external influence factors in a network environment are identified; constructing an output feedback controller based on a dynamic memory event triggering mechanism; a convex hull method is adopted to process saturation nonlinear characteristics of the actuator, a closed-loop system is obtained in combination with the state-space equation, and a guaranteed cost function is designed; and judging whether the closed-loop system meets the requirements of local asymptotic stability and a preset weighted disturbance attenuation level, solving a linear matrix inequality, and obtaining an output feedback controller gain and an event trigger weight matrix. The objective of the invention is to solve the problem that the system stability is difficult to guarantee under the complex conditions that a power system suffers from DoS attacks, actuator saturation exists and external disturbance faces.

The invention discloses a motor sliding mode control method and system based on an equivalent input disturbance observer. The method comprises the following steps: firstly, proposing a basic dynamic equation of the surface-mounted permanent magnet synchronous motor on a two-phase synchronous rotation orthogonal coordinate system, introducing a speed tracking error, and establishing a mathematical model of a singular perturbation system; then, an equivalent input disturbance observer is constructed and used for estimating lumped disturbance of the servo system in real time, and convergence conditions of the observer are given; and finally, obtaining the H-infinity performance of the closed-loop system based on the Lyapunov stability theory, and determining the gain matrix of the non-cascade sliding mode controller according to the corresponding linear matrix inequality. The method effectively improves the control performance and the anti-interference capability of the driving system, and is suitable for the design of a high-performance servo control system of the permanent magnet synchronous motor.

The application provides an environment adaptive formation control method based on a free parameterization stable network, automatically switches between a compact formation and a standard formation according to real-time distances from a formation geometric center to obstacles, and realizes intelligent reconstruction of a formation shape through a preset distance threshold and a smooth transition mechanism; a free parameterization stable network architecture is used to realize parameterization dynamic operator design of each spatial distributed control unit, distributed information exchange is realized through a sparse interconnection topology isomorphic to a spatial system communication graph; inherent stability properties of the free parameterization stable network structure are used to construct a controller parameter unconstrained scheme suitable for a space environment, so that the stability of a spatial closed loop system can be guaranteed for any parameter value, thereby avoiding feasibility constraints of linear matrix inequalities, and realizing unconstrained gradient learning of a three-dimensional distributed controller.

This application provides a method and apparatus for frequency-tolerant control of a specified performance load in a multi-regional power system. The method includes: establishing a system model of the multi-regional power system; obtaining specified performance indicators for frequency deviation for each control area; converting the specified performance indicators into auxiliary variables through mathematical transformation; constructing a stability function for the multi-regional power system and performing stability analysis to obtain a set of linear matrix inequalities concerning the controller gain matrix of each control area; wherein the stability function is configured to satisfy the convergence of system state variables; and the frequency deviation satisfies the specified performance indicators and the system's H under non-zero initial conditions. ∞ The norm is less than the preset performance index; by solving a system of linear matrix inequalities, the controller gain matrix of each control region is obtained to construct the fault-tolerant controller corresponding to each control region for load frequency control. This application provides a load frequency control scheme for multi-region power systems that balances robustness, fault tolerance, and dynamic quality.

The invention discloses a continuous variable multimode quantum entanglement generation chip and method based on an optical frequency comb. The device comprises a multi-frequency coherent frequency comb unit, a programmable optical filter, a micro-ring resonant cavity and a coherent detection regulation and control system, the programmable optical filter filters the multi-frequency coherent frequency comb by using two different channels to obtain multi-frequency coherent pump light and local light, inputs the pump light into the micro-ring resonant cavity, and inputs the local light into the coherent detection regulation and control system; the micro-ring resonant cavity excites a plurality of nonlinear processes below an internal threshold value of the micro-ring resonant cavity under pumping so as to prepare a multimode Gaussian state and input the multimode Gaussian state into the coherent detection regulation and control system; the coherent detection regulation and control system decomposes a multi-mode Gaussian state into a plurality of intrinsic super-modes, and the programmable optical filter adjusts local light according to a decomposition result and a linear matrix of the prepared entangled state so as to control the intrinsic super-modes in a frequency domain and prepare a multi-mode quantum entangled state; and performing frequency locking on the multimode Gaussian state and the local light.

The present invention discloses an adaptive event-triggered control method for a vehicle platoon, belonging to the technical fields of automation and vehicle engineering. The method first establishes a nonlinear dynamic model of a single vehicle. Secondly, graph theory is used to describe the communication topology among vehicles. Then, an adaptive event-triggered mechanism is introduced, and a distributed controller is designed in combination with the adaptive event-triggered mechanism. According to the communication topology, a closed-loop error model of the vehicle platoon is established. Finally, the Lyapunov stability theory and linear matrix inequalities are introduced. According to the closed-loop error model, an H ∞ performance index is introduced to obtain a sufficient condition for ensuring the stability of the vehicle platoon. The present invention ensures the stability of the vehicle platoon, can reduce the communication resource expenditure, improve the performance, and greatly improve the flexibility of data transmission among vehicles.

The present invention discloses a design method for a dynamic event-triggered manipulator system controller based on adjacent modal dependency. With the help of an auxiliary system, the unknown interconnected terms are processed using the cyclic small gain condition, and the closed-loop system is stochastically stable and satisfies H ∞ Sufficient conditions for performance. The relaxation matrix is ​​used to address the nonlinearity caused by adjacent modes, and a new controller design condition is proposed using linear matrix inequalities. Compared with traditional methods, this method can be applied to robotic arm systems with unknown interconnections and does not require knowledge of the real-time operating modes of all subsystems, thus saving considerable costs.

The invention discloses a lossless convexity method for gravitational wave spacecraft formation attitude alignment random optimal control, and the method comprises the steps: setting related parameters in a task scene, including the rotational inertia of a spacecraft, the maximum thrust moment, the initial state and target state of the spacecraft, the pointing constraint, and a disturbance coefficient matrix; establishing a random spacecraft attitude dynamic model; utilizing opportunity constraints to describe a plurality of constraints with uncertainty, including moment constraints, taboo constraints and forced constraints; converting a non-convex part in the constraint condition into a linear matrix inequality (LMIs) by adopting the Schel complement theorem, and adding a virtual control variable and a penalty term to obtain a convex problem which can be directly solved by using the CVX; the invention aims to realize random optimal control of gravitational wave spacecraft formation attitude alignment through a convex optimization method.

The invention provides an H infinite dynamic output feedback control method of an SS type IPT system. The method comprises the following steps: constructing an extended description function state space model of the SS type IPT system; an integral error between a reference signal and actual output is introduced on the basis, and an augmented system model is established in combination with external disturbance and measurement noise; based on a Lyapunov function and an H infinity performance index, sufficient conditions of asymptotic stability and disturbance suppression performance of a closed-loop system are deduced and converted into a linear matrix inequality to be solved, so that gain parameters of a dynamic output feedback controller are directly obtained. Under the condition that external disturbance and measurement noise exist, accurate tracking of the reference signal by the system load voltage can still be guaranteed, the robustness and the fault-tolerant capability of the system are improved, meanwhile, dependence on alternating current side variable measurement is avoided, and the method has high engineering application value.

The invention discloses a fault-tolerant control method based on a polyhedral uncertain interconnection system, and the method comprises the steps: building a spatial interconnection system state space model with polyhedral uncertainty and external interference, and constructing a dynamic model through representing an actuator fault as a structured uncertainty parameter with a known boundary; constructing an iterative learning control increment model containing an actuator fault based on the model, and defining a system operation batch, a finite time period, an expected trajectory and a tracking error; designing an I LC updating law, and further exporting a linear discrete repetition process model represented by an extended state vector; for repetitive and non-repetitive disturbances, calculating a controller gain matrix which ensures that the system has robust stability and H-infinity performance indexes by solving a linear matrix inequality; the high-precision tracking performance and the strong fault-tolerant capability of the system under the conditions of multi-source uncertainty, interference and actuator faults are verified through online experimental operation and root mean square error calculation.

The application discloses an airplane longitudinal fault-tolerant control and reconstruction method under the condition of elevator surface failure and a related device, and belongs to the technical field of aircraft fault-tolerant control.The airplane longitudinal fault-tolerant control and reconstruction method continues to describe the process of airplane elevator sudden failure by using a Markov process.Then, the application establishes a mathematical model of an airplane longitudinal attitude control system with Markov jump characteristic faults.In consideration of the uncertainty of the system model and external disturbance, the application utilizes a sliding mode control technology to propose a fault-tolerant control scheme for the established airplane longitudinal attitude control system with Markov jump characteristic faults.Compared with some existing sliding mode controller design methods, the method proposed by the application needs to solve a smaller number of linear matrix inequalities.Finally, simulation tests show that the fault-tolerant control method designed by the application is effective and advantageous in airplane longitudinal attitude control.