86 results about "Linear quadratic" patented technology

A dynamic wireless charging system optimal control method based on accurate output regulation comprises the following steps: constructing an external system capable of generating an interference signal and a reference signal by using an accurate output regulation theory and aiming at the interference and constant reference voltage suffered by an energy receiving end Boost type DC-DC converter in an electric vehicle dynamic wireless charging system; therefore, a system control problem is converted into an output adjustment problem; and designing a state feedback controller based on the constructed external system and the mathematical model of the DC-DC converter, optimizing a state feedback gain parameter by means of a linear quadratic regulator (LQR), and finally obtaining an optimal state feedback controller. According to the method, the influence of large-range energy disturbance caused by movement of the electric vehicle on the system can be effectively restrained, optimal adjustment of system output can be achieved, and the method has practical engineering application prospects.

This application provides an automatic parking trajectory tracking control method, storage medium, and electronic device. The method includes: determining the current nearest point and shift point closest to the origin of the vehicle coordinate system from a sequence of discrete trajectory coordinate points; determining at least one preview point based on the current nearest point, and obtaining the vehicle's lateral deviation and heading angle deviation based on the preview point; establishing kinematic equations with lateral deviation and heading angle deviation as state variables, and obtaining discretized state-space equations; constructing an offline parameter table of different vehicle speeds and corresponding state feedback values ​​based on the discretized state-space equations and a preset linear quadratic regulator; obtaining the corresponding vehicle rotation value according to the real-time vehicle speed and the offline parameter table; and performing automatic parking control based on the gear information of the current nearest point and the current vehicle rotation value. This application effectively solves the technical problem of difficulty in simultaneously achieving accuracy, real-time performance, and robustness in existing automatic parking trajectory tracking control methods.

The invention discloses a rigid-flexible coupling system modeling and self-adaptive control method based on data driving, and belongs to the field of space tethered robots. The method comprises the following steps: constructing a physical simulation model of the space tethered robot, and collecting state variables and control input data of system operation to construct a training data set; on the basis of the Kupman operator theory, constructing a mapping model from a nonlinear system to a dimension raising linear system with a deep neural network as an embedded function, and training the mapping model on the basis of the training data set; designing a linear quadratic optimal controller; under a reinforcement learning framework, a strategy optimization target taking controller parameters and model parameters as optimization objects is constructed, and collaborative adaptive adjustment of the model parameters and the controller parameters is realized through iterative updating. According to the invention, the optimal control of the space tethered robot is realized.

This invention discloses a fault-tolerant and vibration suppression control method for rigid-flexible coupled robots based on synchronous disturbance observation and dynamic event triggering. The method includes: establishing a large-deformation dynamic model of the rigid-flexible coupled robot mechanism and constructing rigid coordinates, flexible modal coordinates, and control targets; establishing an actuator effectiveness decay fault model and transforming the original underactuated system into an equivalent fully actuated model oriented towards trajectory tracking; designing a fixed-time synchronous disturbance observer based on error dynamics to estimate external disturbances and composite uncertainties online; constructing a dynamic event triggering mechanism and a time-synchronous fault-tolerant sliding mode control law to achieve synchronous convergence of the system state to the sliding surface within a fixed time; introducing a hybrid reference trajectory and virtual input to establish an augmented state model and designing a robust linear quadratic state feedback controller. This invention achieves coordinated control of trajectory tracking and flexible vibration suppression under conditions of external disturbances, actuator failures, and limited communication resources.

The invention discloses a posture control method and system of a discrete gravity center double-wheel-foot robot and a storage medium, and relates to the technical field of gravity center control. Discrete configuration and rapid switching of the gravity center position are achieved by actively adjusting hip joints and knee joints, and a robot model is established based on multi-rigid-body dynamics; simplifying the model into an inverted pendulum linear model family with parameters changing along with the gravity center in the front-back direction; a plurality of discrete gravity center working conditions are preset, each working condition corresponds to a specific joint target angle and model parameters, and the optimal working condition is selected for switching according to the real-time posture and the motion state; and designing a cooperative control law by adopting a linear quadratic regulator, and finally, realizing stable attitude control of the robot under complex terrains and disturbances through multi-joint cooperative execution. According to the method, the disturbance rejection capability and the attitude stability margin are remarkably improved through discrete gravity center configuration, meanwhile, the model complexity and the real-time calculation burden of continuous gravity center adjustment are avoided, and control performance and engineering realizability are achieved at the same time.

The invention discloses a method for optimizing the thickness of an electrolyte and a cathode and improving the energy efficiency of SOECs. The method specifically comprises the steps of electrochemical modeling of SOEC considering current leakage, prediction of working potential needed by the SOEC during operation, building of an electrolytic cell energy efficiency model, building of a residual stress model based on the SOEC and building of a thermal-electric-chemical-mechanical coupling stress model. Two optimization problems are formulated by considering the volatility of renewable energy sources, the optimization problems are combined with a nonlinear quadratic programming SQP algorithm and a particle swarm optimization PSO algorithm to be converted into a wanted standard optimization problem, the optimal electrolyte thickness and cathode thickness are obtained, the optimal electrolytic cell energy efficiency is obtained, and the optimal energy efficiency of the SOEC is achieved. According to the method, hydrogen production and energy efficiency improvement can be reasonably balanced, stress safety is guaranteed, and valuable guidance is provided for design and development of SOEC.

The application provides a privacy protection method of a linear quadratic control system based on model disturbance, and comprises the following steps: intentionally informing a cloud of an incorrect system model according to the problem setting that system knowledge between the cloud and a client is asymmetric; introducing a system observation matrix error, and widening the coverage of the privacy protection method design under the condition that the system knowledge between the cloud and the client is asymmetric according to the existing state estimation inherent error boundary and the existing privacy protection method; the client sends processed data to the cloud instead of the original information sequence of the local system; and according to a linear quadratic Gaussian problem, the influence of the collaborative design of the linear transformation and the model parameter disturbance on the privacy protection and control performance trade-off is obtained.

This invention provides a control method for a lower limb exoskeleton rehabilitation robot based on the sliding mode optimization method, belonging to the field of medical rehabilitation robot control technology. The method includes: establishing a two-degree-of-freedom dynamic model of the lower limb exoskeleton rehabilitation robot, and transforming it into a linear state-space model using feedback linearization technology; designing a linear quadratic regulator (LQR) for the linearized model to obtain the optimal feedback gain matrix; constructing an integral sliding surface containing the optimal feedback gain matrix, so that the equivalent control law of the system in the sliding mode possesses the globally optimal dynamic performance of the LQR; and based on adaptive preset time theory, constructing a sliding mode reaching law and an adaptive gain update law containing novel nonlinear functions to generate the final control torque.

The invention discloses an ultra-low orbit satellite electric propeller two-stage cascade power overall planning control method, and relates to the technical field of satellite electric propellers, and the method comprises the steps: constructing a thrust-radio frequency power matching model; utilizing an extended Kalman filtering algorithm to carry out radio frequency source power dynamic estimation technology research, and constructing a state observer; based on a thrust-radio frequency power matching model and a state observer, constructing a self-adaptive predictive power control framework based on measured data and dynamic state estimation; determining a power coupling mechanism between the spiral wave radio frequency source and the ion cyclotron resonance heating radio frequency source, and constructing a front-stage and back-stage power linkage relation mathematical model; based on a front-stage and back-stage power linkage mathematical model, a dynamic power optimal distribution method with optimal efficiency, thrust and specific impulse under power constraint is established, and a feedback controller based on delay compensation linear quadratic Gaussian control is constructed. And the performance of the ultra-low orbit satellite electric propeller is optimized.

The invention discloses a data processing method and device for a vehicle active suspension, terminal equipment and a storage medium, and belongs to the field of suspension control, and the method comprises the steps: obtaining driving related data and initial grey wolf optimization algorithm parameters of a to-be-controlled vehicle; constructing a random pavement model, an active suspension model and a braking system model of the to-be-controlled vehicle according to the driving related data; determining a state space matrix according to the active suspension model; determining an initial grey wolf set based on the initial grey wolf optimization algorithm parameters, taking the initial grey wolf set as input of a first grey wolf optimization algorithm, repeatedly executing the grey wolf optimization algorithm, and outputting optimal grey wolf optimization algorithm parameters; and determining an optimal linear quadratic regulator based on the optimal grey wolf optimization algorithm parameter, and controlling the active suspension of the to-be-controlled vehicle, so that the problem of poor riding experience feeling caused by the fact that the active suspension is not matched with the driving condition in the prior art can be solved.

The present application belongs to the field of aircraft flight control, and particularly relates to a kind of finite time flight height control method of integrated flap direct force control.The finite time flight height control method of integrated flap direct force control according to height control reference trajectory, establishes the linear dynamics model of the longitudinal channel of the controlled aircraft;According to the flight control target, a finite time domain linear quadratic optimal control problem is established, and the corresponding two-point boundary value problem is derived;Using finite-time iteration algorithm, the optimal flight state and control solution of flight height control are obtained;The optimal solution is applied to height control.The finite time flight height control method of integrated flap direct force control uses finite-time iteration to obtain optimal control instructions, and through parallel computing, efficient solution of height and heading position control instructions is realized, which has engineering practical value.

The application discloses a kind of unmanned aerial vehicle flight control methods based on adaptive quasi-optimal high-order sliding mode control, including obtaining the first pose vector of unmanned aerial vehicle to be controlled;The first pose vector is used as the input of preset pose control model, and the control signal output by the preset pose control model is obtained according to the preset integral sliding surface of the preset pose control model and preset control rate, wherein the preset pose control model is the preset second-order integral chain model with pose as state variable, and the preset control rate makes the state variable of the preset second-order integral chain model reach the preset equilibrium state, and the preset linear quadratic index is minimum;The unmanned aerial vehicle to be controlled is controlled according to the control signal.The method of the application can guarantee that the tracking error of closed-loop system converges in finite time.

The embodiment of the invention provides an alternating current servo system control method, system and device based on an internal model principle and a medium, and belongs to the technical field of motor control. The method comprises the following steps: performing mechanism analysis, system identification and model order reduction processing on the alternating current servo system to obtain a four-order model corresponding to the alternating current servo system; on the basis of the fourth-order model, designing the corresponding optimal state feedback of the AC servo system under a linear quadratic regulator; determining a state observer of the inner ring object model, and determining an optimal observer parameter by using a first LQ criterion function according to the state observer; determining a first state space expression corresponding to the AC servo system according to the optimal state feedback and the optimal observer parameter; and determining a target control parameter corresponding to an optimal controller of the AC servo system according to the first state space expression, so that the AC servo system realizes optimal control according to the target control parameter.

The application discloses a spacecraft magnetic moment attitude control method based on a non-inverse iteration algorithm, and the method establishes a linear periodic model for a spacecraft attitude control system which only relies on a magnetic moment; on the basis, according to a linear quadratic optimal control theory, an optimal controller design problem is converted into a solution problem of a discrete periodic Riccati equation associated with the optimal controller design problem; on the basis of a gradient descent principle, an error function is constructed, and a non-inverse iteration algorithm based on the gradient descent principle is proposed to solve the discrete periodic Riccati equation, so that a matrix inversion operation in a traditional solution method is avoided, and the calculation efficiency and the numerical stability are effectively improved; the obtained Riccati equation solution is used to obtain an optimal state feedback control law, so that the spacecraft attitude optimal control only using the magnetic moment is realized, and a new solution scheme is provided for an attitude control problem of a limited actuator in a space task.

The invention discloses an amphibious vehicle cluster autonomous cooperation method based on LQR control, and the method comprises the steps: (1) a master vehicle plans an expected trajectory from a starting position to a task position, takes the expected trajectory as a global reference trajectory, and transmits the global reference trajectory to each slave vehicle; (2) each slave vehicle determines an expected trajectory based on the relative pose of the slave vehicle and the master vehicle and the global reference path; and (3) the master vehicle and the slave vehicle control the vehicle to track an expected trajectory through a linear quadratic regulation control algorithm. According to the method, a control strategy of centralized planning and distributed execution is adopted, when a vehicle operation medium changes, the structure of a linear quadratic regulation (LQR) control algorithm is not changed, and corresponding model parameters and an LQR weight matrix are switched to adapt to different environments; and meanwhile, the smoothness of switching from underwater to land or from land to underwater is greatly improved.

The invention relates to the technical field of multi-agent driving control, in particular to an uncertain nonlinear agent driving control method based on linear quadratic adjustment, and the method comprises the steps: deducing a standard differential equation mathematical model according to an uncertain nonlinear kinematics model of a guider, thereby independently listing unmeasurable nonlinear items; a non-measurable nonlinear item is estimated through an observer, a dynamic tracking controller is designed based on the observer, and the input state stability of the system is ensured in combination with a multi-loop nonlinear small gain condition, so that a guider can track a time-varying reference signal. Then, a reference signal generating system which generates a variable reference signal at the moment is used as a new guider, a drive control controller is designed through linear quadratic adjustment, so that optimal input is solved through state estimation and error optimization, an uncertain nonlinear drive control problem is simplified to be a linear quadratic adjustment problem to be solved, and the drive control precision is improved. The integrated collaborative design of'tracking the reference signal by the guider 'and'arriving the target position by the rover' is realized.

This invention primarily relates to the field of thermal power unit system technology, specifically a method for identifying a closed-loop optimized control system for a deep peak-shaving thermal power unit. The method includes: S100 establishing a spatial state model of the thermal power unit system; S200 designing linear quadratic controller parameters for the spatial state model of the thermal power unit system, calculating the optimal control law through a state feedback matrix, and forming a closed-loop system of the thermal power unit; and obtaining the control input, control output, and system setpoint of the closed-loop system; S300 decomposing the closed-loop system into two open-loop subsystems; S400 obtaining the sensitivity function of the closed-loop system by performing subspace identification on the control input and system setpoint, and constructing a noise-free intermediate signal using the sensitivity function; and S500 obtaining a consistent and unbiased estimate of the parameters of the thermal power unit system by performing subspace identification on the intermediate signal and the control output of the closed-loop system.

The invention discloses a near-surface X-rudder autonomous underwater vehicle control method based on sea wave interference observation, and the method comprises the steps: collecting a measurement signal of X-rudder autonomous underwater vehicle measurement equipment, and obtaining the attitude data of an underwater vehicle; each rudder blade of the X-rudder autonomous underwater vehicle is numbered, and an underwater vehicle motion model is established; according to the state-space equation of the underwater vehicle motion model and the attitude data of the underwater vehicle, establishing a linear quadratic regulator control model to obtain a first control rate; establishing a sea wave interference observer, observing and estimating the interference of the sea current on the aircraft, establishing a nonlinear passive estimator model based on an observation result, and obtaining a second control rate; and establishing a rudder force distribution model of the underwater vehicle, obtaining an expected rudder angle of each rudder blade of the X-rudder autonomous underwater vehicle based on the first control rate and the second control rate, and realizing control of the vehicle. According to the method, the problem of tracking errors of the autonomous underwater vehicle caused by ocean current disturbance can be solved.

This invention provides an adaptive admittance method and system based on the optimal control LQR theory, including constructing an environmental dynamics model and a robotic arm admittance control model, and deriving their interactive dynamics model; defining state variables and control inputs, and establishing a standard form state-space equation; constructing a quadratic performance index function, transforming admittance parameter optimization into an LQR problem; substituting the linear quadratic regulator framework into the quadratic performance index function, transforming the LQR problem into solving the Riccati matrix differential equation, and deriving analytical expressions for virtual optimal stiffness and virtual optimal damping; within the robotic arm control sampling frequency, inputting real-time collected environmental contact forces and the actual pose of the robotic arm end effector, along with set weighting coefficients, into the analytical expressions to calculate optimal virtual stiffness and damping; and then calculating pose corrections based on the admittance control model to correct the robotic arm's motion trajectory.

The invention discloses a trajectory tracking and stability cooperative control method for a multi-axis distributed driving vehicle, and provides a hierarchical control architecture. The upper-layer trajectory tracking controller comprises a self-adaptive preview linear quadratic regulator based on fuzzy logic reasoning, and the self-adaptive preview linear quadratic regulator dynamically adjusts the preview distance according to the vehicle speed and the acceleration and outputs a steering angle instruction; and the seven-section S curve speed planner generates a smooth speed and acceleration curve. The lower-layer stability and torque distribution controller comprises an equivalent sliding mode controller for calculating an additional yaw moment based on the yaw velocity and the side slip angle error; and based on a torque distributor of quadratic programming, introducing an inter-axle yawing moment coefficient as a geometric constraint, tracking a required torque, and minimizing a tire attachment utilization rate and a slip rate as a target distribution torque. Through cooperation of the upper layer and the lower layer, high-precision trajectory tracking, high robust stability and longitudinal smoothness are considered, and the comprehensive performance of the multi-axle vehicle under the limiting working condition is remarkably improved.

The invention provides a time-lag industrial process tracking control method based on inner and outer ring singular perturbation decomposition, and the method comprises the steps: firstly building a cascade singular perturbation time-lag system model for an industrial process containing fast and slow dynamic states and time lag, and decomposing a tracking problem into an optimal tracking problem of an outer ring slow subsystem and an inner ring fast subsystem based on a singular perturbation theory; linear quadratic tracking is converted into an adjustment problem by constructing an auxiliary system, and an optimal controller theoretical form is deduced. The condition that model parameters are difficult to obtain is considered, a data-driven reinforcement learning algorithm is designed for inner and outer ring operation layers, a compact equation least square solution converted by a Riccati equation is solved through input and output data, and an optimal control strategy is learned. And finally, the learned controller is utilized to realize the optimal tracking of the given signal by the system. The method does not depend on system prior information, solves the problem of traditional control in a multi-scale and time-delay coupling system, improves the control precision and response speed of a complex industrial process, and has important application value in the field of production automation.

The invention discloses a vehicle body stability control method and system and a vehicle, the vehicle body stability control method is applied to the vehicle body stability control system, and the method comprises the steps that the current balance state of a vehicle body of the vehicle is judged according to obtained driving parameters; when the vehicle body is in a non-equilibrium state, acquiring an optimal control vector according to the state-space equation and by utilizing a linear quadratic model; according to the optimal control vector, calculating a repair value of a steering wheel turning angle of vehicle body balance; and controlling the steering wheel of the vehicle to be automatically adjusted and repaired according to the repair value of the steering wheel corner. When it is detected that the vehicle deviates from the balance state due to external disturbance in the running process, the optimal control vector is obtained through calculation to conduct direction adjustment, so that the vehicle recovers the balance state, and safe running of the vehicle is guaranteed.

The invention discloses a model identification and damping control method and system for a network-forming converter, and belongs to the technical field of power systems. The method comprises the following steps: injecting a pre-generated test signal sequence into an active power reference instruction of a network-forming converter to excite a system to generate a dynamic response; response data of the system under excitation of the test signal sequence is collected, and the response data and the test signal sequence form an evolution type time sequence data set; based on the evolution type time sequence data set, an equivalent linear model for describing system dynamics is calculated through a Koopman operator identification method; calculating to obtain a state feedback gain matrix by solving a linear quadratic optimal control problem; generating a damping control signal based on the state feedback gain matrix and system state data acquired in real time, and superposing the damping control signal to a control instruction of the network-forming converter; according to the method, the risk of performance reduction and even instability caused by model mismatch in a traditional method is overcome.

The application discloses a satellite sailboard deployment joint simulation method based on MATLAB and ADAMS, first, a satellite sailboard deployment dynamics simulation system is constructed based on ADAMS software, second, a multi-board deployment simulation model of the satellite sailboard is established by using a second Lagrange method, and a dynamics model of the system is obtained; next, Runge-Kutta with four-order high precision is used to solve the dynamics differential equation by using MATLAB software, and a deployment process of the satellite sailboard and a response result of the satellite sailboard subjected to impact are given; then, ADAMS dynamics simulation results (S1) are compared with theoretical model results (S3), and the accuracy of the dynamics theoretical model is verified within a certain error; finally, an optimal control law of state linear feedback of the satellite sailboard deployment system is derived based on a linear quadratic regulator (LQR) control algorithm; the application solves the problem that the satellite sailboard cannot be quickly and stably deployed, and can provide certain theoretical guidance for the structural design and on-orbit deployment of the space satellite sailboard.

The present invention belongs to the field of trajectory control optimization, and specifically relates to an optimization method for a gliding missile controller based on an improved Gray Wolf algorithm. The method comprises the following steps: Step (1): Based on the dynamic characteristics analysis of the gliding missile, a disturbance motion equation of the missile body is established and simplified; Step (2): Based on the simplified disturbance motion equation of the missile body, under the conditions of zero interference and zero initialization, a suitable input control quantity and state vector are selected to construct its longitudinal state equation; Step (3): Based on the system state equation, an LQR linear quadratic regulator is constructed: the parameters of the weighting matrix Q matrix and the R matrix in the LQR linear quadratic regulator are optimized using the Gray Wolf algorithm with a nonlinear convergence factor to obtain the feedback gain matrix K, thereby improving the system response time and the stability of the new control system. The present invention optimizes the trajectory and improves the system response by selecting some parameters in the longitudinal disturbance equation as state variables and optimizing the feedback gain, thereby improving the stability margin of the system.

A sequence of input samples that are measures of position or orientation of an input device being held by a user are received. A current output sample of a state of linear quadratic estimator, LQE, is computed that is an estimate of the position or orientation of the input device. The current output sample is computed based on i) a previously computed output sample, and ii) a velocity term. An updated output sample of the state of the LQE is computed, based on i) a previously computed output sample, and ii) a new input sample. Other embodiments are also described and claimed.

The application discloses a spacecraft escort problem solving method based on LQR and differential game, constructs a game model of the escort problem based on a CW equation, and comprises a cost function, optimization variables, dynamic constraints, acceleration capacity constraints and the like; the cost function adopts a linear quadratic index, the optimization variables are continuous control force accelerations of both attack and defense sides, the dynamic constraints are described by using the CW equation, and the acceleration capacity constraints are modeled by using maximum acceleration limitation; the method has the advantages of simple model, clear physical meaning and convenient solving; in addition, the application converts a complex non-zero-sum game problem into a phased zero-sum game problem and an optimal control problem, can effectively solve the spacecraft escort problem under the action of continuous thrust, is an effective expansion of a continuous thrust escort problem model and method in the prior art, and significantly improves the solving efficiency of the problem. Through the method, an effective cooperative defense threat solution can be provided for on-orbit spacecraft.

The application belongs to the field of vehicle driving assistance, and specifically provides a lateral path tracking method and device based on adaptive weight coefficients, equipment and storage medium, the method comprises the following steps: calculating the front wheel steering angle through the linear quadratic regulation algorithm in the upper controller; calculating the control variable to eliminate the feedback error through the feedforward control; using the improved sliding mode control algorithm to design the stability compensation controller of the additional torque, calculating the additional yaw moment for the compensation of the total driving torque; judging the current stability state through the phase plane of the center of mass side slip angle and the yaw angular velocity, and automatically adjusting the weight of the phase plane based on the judgment result of the stability state; calculating the distribution of the additional yaw torque in real time through the adaptive adjusted weight coefficient. Through the sliding mode control theory, the stability is determined. Through the adaptive adjustment of the weight coefficient, the additional yaw torque is calculated in real time, and the control stability is improved.

The application discloses a strip plate shape intelligent regulation and control method based on an adaptive fusion model, which comprises the following steps: step 1, collecting historical rolling production process data and performing pretreatment; step 2, constructing a rolling production process data set based on the pretreated data; step 3, classifying plate shape quality according to the ratio of strip crown and target thickness and setting a category label; step 4, establishing an adaptive strip outlet plate shape diagnosis model containing multiple classifiers based on a DS theory, and training the diagnosis model through the rolling production process data set; step 5, inputting rolling production process data under a new rolling schedule into the classifier of the trained adaptive strip outlet plate shape diagnosis model to obtain a real-time classification prediction result of the strip, and if the prediction classification is under-crown or over-crown, step 6 is executed; otherwise, the process parameters are not adjusted; and step 6, dynamically adjusting and optimizing the process parameters based on an inverse linear quadratic control (ILQ) according to the prediction result of step 5.

This invention provides a dual-motor steer-by-wire system and its active fault-tolerant control method. The method includes: a front wheel steering angle tracking controller, a vehicle stability controller, and a nonlinear model control method based on a variable parameter (LPV) model. The front wheel steering angle tracking controller and the stability controller are designed based on a linear quadratic regulator (LQR) and an optimal control algorithm, including: solving for the ideal front wheel steering angle; establishing a dynamic model of the dual-motor steering actuation system; and designing the steering angle tracking controller and the stability controller based on the ideal front wheel steering angle and the steering system dynamic model. The dual-motor active fault-tolerant control includes: comparing the control torque output by the dual-motor torque sensors with that output by the front wheel steering angle tracking controller, calculating the fault coefficient, and optimizing the steering actuator model into a variable parameter (LPV) nonlinear structure containing motor fault parameters. This invention can ensure vehicle safety after a dual-motor failure.