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Minimal time closed loop controller design for linear systems with bounded control amplitudes and rates using approximate functional expression
This note investigates the closed-loop stability of linear, time-invariant systems controlled by linear-quadratic-Gaussian (LQG) type controllers, when the actuators have nonlinearities. The nonlinearities N(sigma) are assumed to violate the standard LQ robustness condition either for values of sigma away from sigma = 0, or in a neighborhood of sigma = 0. The cases with an exponentially stable state estimator, and an estimator with ultimately bounded estimation error are considered, and expressions are obtained for the regions of attraction and ultimate boundedness.
The decentralized stochastic control of a linear dynamic system consisting of several subsystems is considered. A two-level approach is used by the introduction of a coordinator who collects measurements from the local controllers periodically and in return transmits coordinating parameters. Two types of coordination are considered: open-loop feedback and closed loop. The resulting control laws are found to be intuitively attractive.
A class of optimal linear time invariant tracking systems, both in continuous time and discrete time, of which the number of inputs (which are restricted to be step functions) is equal to the number of system outputs, is studied. Along with derivation of equations and design procedures, two discretization schemes are presented, constraining either the control or its time derivative, to be a constant over each sampling period. Descriptions are given for the linearized model of the F-8C aircraft longitudinal dynamics, and the C* handling qualities criterion, which then serve as an illustration of the applications of these linear tracking designs. A suboptimal reduced state design is also presented. Numerical results are given for both the continuous time and discrete time designs.
A general form of an optimal washout filter is derived using state-space linear optimal control theory, and this is applied to the design of washout filters of various types of moving base motion simulators, including the NASA's vertical motion simulator. Attention is given to the linear elements of a washout filter. One of the nonlinearities considered is braking which may be required near the end of the simulator excursion to prevent a crash. Although the general form of the optimal washout filter is applicable to time-variant system, the applications analyzed in the study are restricted to time-invariant cases.
Feedback control laws are presented for stabilization models of a hoop/column antenna. A brief review of linear and nonlinear feedback control laws is included. A method that is computable on a microprocessor and assures closed loop stability is explained and compared to a linear control law model.
Output feedback control systems design, considering closed loop system sensitivity to plant parameters based on linear optimal control problem
The development of a digital adaptive flight control algorithm is described that combines a weighted least squares estimator with optimal linear regulator control logic designed to minimize a quadratic model following performance index. Very promising results for a typical fighter aircraft's trajectory over six distinct flight conditions are reported.
A procedure is presented for the active control of a spinning flexible spacecraft. Such a system exhibits gyroscopic effects. The design of the controller is based on modal decomposition of the gyroscopic system. This modal decoupling procedure leads to a control mechanism implemented in modular form, which represents a distinct computational advantage over the control of the coupled system. Design procedures are demonstrated for two types of control algorithms, linear and nonlinear. The first represents classical linear feedback approach, and the second represents an application of on-off control, both types made feasible by the modal decomposition scheme.
A procedure is presented for the active control of a spinning flexible spacecraft. Such a system exhibits gyroscopic effects. The design of the controller is based on modal decomposition of the gyroscopic system. This modal decoupling procedure leads to a control mechanism implemented in modular form, which represents a distinct computational advantage over the control of the coupled system. Design procedures are demonstrated for two types of control algorithms, linear and nonlinear. The first represents classical linear feedback approach and the second represents an application of on-off control, both types made feasible by the modal decomposition scheme.
Graph theoretic techniques are used to study controllability of linear systems which represent large flexible orbiting space systems with inherent damping. The controllability of the pair of matrices representing the system state and control influence matrices is assured when all states in the model are reachable in a digraph sense from at least one input and also when the term rank of a Boolean matrix whose non trivial components are based on the state and control influence matrices has a term rank of the order of the state vector. The damping matrix does not influence the required number of actuators but gives flexibility to the possibility locations of the actuators for which the system is controllable.
Switching times updated to minimize errors in final positions. Algorithm computes "bang-bang" control laws for single- or multiple-input systems, both those describable by linear dynamical equations and those describable by nonlinear dynamical equations that are linear in control vectors. Algorithm needed because analytical solutions of "bang-bang" control problems intractable for all but simplest systems.
Simulation and analysis for modern engineering systems now routinely requires the merging of multiple disciplines, physical-domains, time-scales, and data sets — all at ever increasing levels. These capabilities are especially needed in the domain of Advanced Air Mobility, where rapidly emerging vehicle designs are significantly more complex, while having to be both cost-effective and safe. To meet these engineering challenges, machine learning methods are an attractive option for merging models and data across multiple areas while providing uncertainty quantification and maintaining computational efficiency. This paper examines the use of Gaussian process machine learning to generalize and enhance the commonly used class of quasi-Linear Parameter Varying models for fast full-envelope simulation while also supporting control system design and analysis with model uncertainty. Gaussian process machine learning is selected because it: can fuse multiple data sets, enables an easy trade-off between data fitting and smoothing, provides model uncertainty quantification, scales well with increasing complexity, and does not generally require starting from a large training data set. To demonstrate the benefits of the approach, a robust stability analysis with Gaussian process uncertainty is shown for a NASA reference design of an electric quad-rotor air-taxi concept vehicle with motor parameter uncertainty.
A stability and control augmentation system (SCAS) was designed based on a set of comprehensive performance criteria. Linear optimal control theory was applied to determine appropriate feedback gains for the stability augmentation system (SAS). The helicopter was represented by six-degree-of-freedom rigid body equations of motion and constant factors were used as weightings for state and control variables. The ratio of these factors was employed as a parameter for SAS analysis and values of the feedback gains were selected on this basis to satisfy three of the performance criteria for full and partial state feedback systems. A least squares design method was then applied to determine control augmentation system (CAS) cross feed gains to satisfy the remaining seven performance criteria. The SCAS gains were then evaluated by nine degree-of-freedom equations which include flapping motion and conclusions drawn concerning the necessity of including the pitch/regressing and roll/regressing modes in SCAS analyses.
Magnetic torquing of spacecraft has been an important mechanism for attitude control since the earliest satellites were launched. Typically a magnetic control system has been used for precession/nutation damping for gravity-gradient stabilized satellites, momentum dumping for systems equipped with reaction wheels, or momentum-axis pointing for spinning and momentum-biased spacecraft. Although within the small satellite community there has always been interest in expensive, light-weight, and low-power attitude control systems, completely magnetic control systems have not been used for autonomous three-axis stabilized spacecraft due to the large computational requirements involved. As increasingly more powerful microprocessors have become available, this has become less of an impediment. These facts have motivated consideration of the all-magnetic attitude control system presented here. The problem of controlling spacecraft attitude using only magnetic torquing is cast into the form of the Linear Quadratic Regulator (LQR), resulting in a linear feedback control law. Since the geomagnetic field along a satellite trajectory is not constant, the system equations are time varying. As a result, the optimal feedback gains are time-varying. Orbit geometry is exploited to treat feedback gains as a function of position rather than time, making feasible the onboard solution of the optimal control problem. In simulations performed to date, the control laws have shown themselves to be fairly robust and a good candidate for an onboard attitude control system.
Low-authority control or vibration suppression in large, flexible space structures can be formulated as a linear feedback control problem requiring computation of displacement and velocity feedback gain matrices. To ensure stability in the uncontrolled modes, these gain matrices must be symmetric and positive definite. In this paper, efficient computation of symmetric, positive-definite feedback gain matrices is accomplished through the use of multiple-constraint matrix update techniques originally developed for structural identification applications. Two systems were used to illustrate the application: a simple spring-mass system and a planar truss. From these demonstrations, use of this multiple-constraint technique is seen to provide a straightforward approach for computing the low-authority gains.
In this project, work has been done in the field of conceptual design of experimental tiltrotors. The main tools that have been used are NDARC (NASA Design and Analysis of Rotorcraft) and SIMPLI-FLYD. NDARC is a conceptual design tool for rotorcraft, and it is used to find trim points under various flight conditions. SIMPLI-FLYD is an integrated collection of software tools that enables a flight dynamics and control assessment of the rotorcraft vehicle design generated from NDARC. Two different tiltrotors have been investigated. Initially, work was done with the Bell XV- 15 tiltrotor. NDARCs ability to correctly model the tiltwing transition between airplane mode and hover mode was looked into. In addition, data from old flight tests were compared to the NDARC output, to see how accurately performance could be predicted. After the XV-15 analysis, an NDRARC model of a novel tiltwing concept from Elytron Aircraft was written and analyzed together with SIMPLI-FLYD. Elytron 2S is an experimental tiltwing aircraft, consisting of a joined-wing design with a small central wing for the proprotor. An alternative approach to hover control is used, where the typical rotor hub and swash plate are substituted for linear actuators controlling pitch, yaw and roll. The objective with the analysis of Elytron is to obtain a more complete understanding of the maneuverability and possible performance of this alternative aircraft configuration.
When allocating redundant effectors to virtual control commands, linear (generalized inverse) allocators have historically been used on aircraft and spacecraft. While simple to implement, generalized inverses are unable to realize a significant portion of the attainable moments. To address this drawback, the control allocation problem can also be formulated as a linear programming or quadratic programming problem and solved using convex optimization based solvers. These approaches have been shown to access a larger set of attainable moments, however, little work has been done to understand the performance of convex optimization-based control allocation in the presence of parametric model uncertainty. This paper seeks to compare the performance of several control allocation approaches, including two forms of generalized inverse allocators, the pseudo inverse and minimum-variance, and the linear programming and quadratic programming approach in the presence of parametric model uncertainty. The performance of these four allocators were tested on an aircraft model in the presence of realistic parametric model uncertainty and the convex optimization approaches were shown to outperform the generalized inverses.