Rapid Algorithm for Generating Entry Landing Footprints Satisfying the No-Fly Zone Constraint

An online estimation algorithm of landing footprints based on the drag acceleration-energy profile is proposed for an entry hypersonic vehicle. Firstly, based on the Evolved Acceleration Guidance Logic for Entry (EAGLE), drag acceleration-energy profiles are designed. To track the drag acceleration-energy profile obtained by the interpolation, a drag acceleration tracking law is designed. Secondly, based on the constraint model of the no-fly zone, flying around strategies are proposed for different conditions, and a reachable area algorithm is designed for no-fly zones. Additionally, by interpolating the minimum and maximum drag acceleration profiles, the terminal heading angle constraint is designed to realize the accurate calculation of the minimum and maximum downrange ranges by adjusting the sign of the bank angle. In this way, the distribution of landing footprints is more reasonable, and the boundary of a reachable area is more accurate. The simulation results under typical conditions indicate that the proposed method can calculate landing footprints for different situations rapidly and with the good adaptability.

Earthquake Ground Motion Matching on a Small Electric Shaking Table Using a Combined NN-PDFF Controller

Replicating acceleration time histories with high accuracy on shaking table platforms is still a challenging task. The complex interference between the components of the system, the inherent nonlinearities, and the coupling effect between the specimen and the shaking table are among other reasons that most affect the control performance. In this paper, a neural network- (NN-) based controller has been developed and experimentally implemented to improve the acceleration tracking performance of an electric shaking table. The latter is a biaxial shaking table driven by linear motors and controlled by a proportional-derivative-feedforward (PDFF) controller that is very efficient in reproducing displacement waveforms on the detriment of the simulation of the prescribed acceleration ground motions. In order to bypass this shortcoming, a control scheme combining the PDFF as a basic control function with a NN controller which filters the shaking table feedback signal and acts on the drive signal by compensating for acceleration distortions is proposed in this study. Several experimental tests have been carried out to build a database for offline training, validating, and testing of the proposed NN control model. Subsequently, the well-trained NN is implemented in the inner control loop of the shaking table to compensate, in parallel with the PDFF controller, the distortions during the replication of acceleration signals. Results of tests using earthquake records showed an enhancement in signal matching when integrating the NN model for both bare and loaded conditions of the shaking table. The tracking errors, estimated using the relative root-mean-square error, between the measured and the desired signal, are significantly reduced in time and frequency domains with the additional NN online controller.

Adaptive acceleration waveform control of two-degree-of-freedom dual electrohydraulic shaking tables

Multi-degree-of-freedom multiple table systems are developed for seismic testing of large-span structures to spread the loads evenly on the tables. Synchronous control of multiple shaking tables is challenging because of coupling between different shaking tables and complex dynamics of the testing systems. This article presents an adaptive waveform control for a two-degree-of-freedom dual electrohydraulic shaking tables testing system to improve the acceleration tracking performance. Synchronous control of the two electrohydraulic shaking tables is transformed into the motion control of a two-degree-of-freedom overconstrained shaking table driven by 10 actuators. The force control loop based on the null space of the Jacobian matrix is developed to reduce the cross-coupling among the actuators. An adaptive acceleration waveform control method based on the DFP optimization algorithm in a complex domain is presented to improve the convergence and stability of the compensation algorithm in the outer control loop and replicate the acceleration reference waveforms accurately. Experimental results obtained in step responses, acceleration frequency responses measurement, and two-degree-of-freedom waveform replication tests are used to demonstrate the effectiveness of the proposed method.

Acceleration decoupling control of 6 degrees of freedom electro-hydraulic shaking table

Electro-hydraulic shaking tables are widely used for vibration testing where high force and displacement amplitudes are required. In particular, they are a vital tool in seismic testing, enabling the development of buildings and other structures which are earthquake resistant. Three-variable-control (TVC) is commonly used for the control of multi-degrees of freedom (DOFs) electro-hydraulic shaking tables. However, the coupling between the DOFs is often significant and is not compensated by TVC. In this paper, an acceleration decoupling control (ADC) method is presented for a 6 DOFs electro-hydraulic shaking table system to improve the acceleration tracking performance and decouple the motion in task space. The gravitational, Coriolis, and centripetal forces are compensated for in joint space based on a dynamic model of the shaking table. Modal control is used to transform the coupled dynamics into six independent systems. Inverse dynamics models are used to cancel the differences in actuator dynamics. The proportional gains in modal space are tuned heuristically to give sufficient stability margins to provide robustness in the presence of modeling errors. The input filter and feedforward controller in TVC are added to improve the acceleration tracking performance of each independent system. Experimental acceleration frequency responses are used to demonstrate the effectiveness of ADC, and in particular these show a consistent reduction in cross-axis coupling compared to TVC. Moreover, only four parameters need to be tuned, as opposed to 36 for TVC, and the method provides a viable route to improving the accuracy of seismic testing in the future.