The matrix minimum principle
Extension of Pontryagin maximum principle and application of matrix minimum principle in solving simple optimal linear regulator problem
MATRIX ANALYSIS↗
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Robust dynamic inversion control laws for aircraft control
Dynamic inversion is a technique for control law design in which feedback is used to simultaneously cancel system dynamics and achieve desired dynamic response characteristics. However, dynamic inversion control laws lack robustness to modeling errors if improperly designed. This paper examines a simple linear example, control of roll rate about the body axis of high performance aircraft, to illustrate some robustness problems which may occur with a simple dynamic inversion control law. The paper demonstrates how structured singular value synthesis techniques can be used to enhance the robustness properties of the dynamic inversion controller.
Balas, Gary J.↗
Robot-Arm Dynamic Control by Computer
Feedforward and feedback schemes linearize responses to control inputs. Method for control of robot arm based on computed nonlinear feedback and state tranformations to linearize system and decouple robot end-effector motions along each of cartesian axes augmented with optimal scheme for correction of errors in workspace. Major new feature of control method is: optimal error-correction loop directly operates on task level and not on joint-servocontrol level.
Bejczy, Antal K.↗
Switching State-Feedback LPV Control with Uncertain Scheduling Parameters
This paper presents a new method to design Robust Switching State-Feedback Gain-Scheduling (RSSFGS) controllers for Linear Parameter Varying (LPV) systems with uncertain scheduling parameters. The domain of scheduling parameters are divided into several overlapped subregions to undergo hysteresis switching among a family of simultaneously designed LPV controllers over the corresponding subregion with the guaranteed H-infinity performance. The synthesis conditions are given in terms of Parameterized Linear Matrix Inequalities that guarantee both stability and performance at each subregion and associated switching surfaces. The switching stability is ensured by descent parameter-dependent Lyapunov function on switching surfaces. By solving the optimization problem, RSSFGS controller can be obtained for each subregion. A numerical example is given to illustrate the effectiveness of the proposed approach over the non-switching controllers.
Switching LPV control↗
Computation of approximate fuel-optimal control
Iterative digital computer determination of optimal fuel control in linear time-invariant plant
ITERATIVE SOLUTION↗
Predictive control and estimation - State space approach
A modified output prediction procedure and a new controller design based on the predictive control law are presented. A new predictive estimator enhances system performance. The predictive controller was designed and applied to the tracking control of the NASA/JPL 70-m antenna. Simulation results show significant improvement in tracking performance over the linear quadratic controller and estimator presently in use.
Gawronski, W.↗
Control of large flexible spacecraft by the independent modal-space control method
The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes.
Meirovitch, L.↗
Non-linear coherent mode interactions and the control of shear layers
A nonlinear integral formulation, based on local linear stability considerations, is used to study the collective interactions between discrete wave-modes associated with large-scale structures and the mean flow in a developing shear layer. Aspects of shear layer control are examined in light of the sensitivity of these interactions to the initial frequency parameter, modal energy contents and modal phases. Manipulation of the large-scale structure is argued to be an effective means of controlling the flow, including the small-scale turbulence dominated region far downstream. Cases of fundamental, 1st and 2nd subharmonic forcing are discussed in conjunction with relevant experiments.
Nikitopoulos, D. E.↗
Integrated structure/control design - Present methodology and future opportunities
Attention is given to current methodology applied to the integration of the optimal design process for structures and controls. Multilevel linear decomposition techniques proved to be most effective in organizing the computational efforts necessary for ISCD (integrated structures and control design) tasks. With the development of large orbiting space structures and actively controlled, high performance aircraft, there will be more situations in which this concept can be applied.
Weisshaar, T. A.↗
Predictive control and estimation algorithms for the NASA/JPL 70-meter antennas
A modified output prediction procedure and a new controller design is presented based on the predictive control law. Also, a new predictive estimator is developed to complement the controller and to enhance system performance. The predictive controller is designed and applied to the tracking control of the Deep Space Network 70 m antennas. Simulation results show significant improvement in tracking performance over the linear quadratic controller and estimator presently in use.
Gawronski, W.↗
Robust integrated flight/propulsion control design for a STOVL aircraft using H-infinity control design techniques
Results are presented from an application of H-infinity control design methodology to a centralized integrated flight/propulsion control (IFPC) system design for a supersonic STOVL fighter aircraft in transition flight. The emphasis is on formulating the H-infinity optimal control synthesis problem such that the critical requirements for the flight and propulsion systems are adequately reflected within the linear, centralized control problem formulation and the resulting controller provides robustness to modeling uncertainties and model parameter variations with flight condition. Detailed evaluation results are presented for a reduced order controller obtained from the improved H-infinity control design showing that the control design meets the specified nominal performance objective as well as provides stability robustness for variations in plant system dynamics with changes in aircraft trim speed within the transition flight envelope.
Garg, Sanjay↗
Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators
The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.
93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗
An activation criterion for repeated use of an optimal fixed time constant energy regulator.
Optimal fixed time constant-energy regulator for linear plants with perturbations operating within bounding hypersurface
REGULATOR↗
Efficient BiVO 4 /CoFeO x H y photoanodes using controlled annealing and conformal linear-sweep electrocatalyst photodeposition
Although monoclinic bismuth vanadate (BiVO 4 ) is a promising photoanode for solar water splitting, its practical use is hindered by imperfect photocurrent generation/collection, low photovoltage compared to the bandgap, and corrosion side reactions that limit durability. Here, we introduce a controlled-annealing sol–gel process for BiVO 4 thin-film photoanodes along with an optimized linear-sweep-voltammetry photodeposition of CoFeO x H y cocatalysts. The resulting BiVO 4 films annealed at 550 °C exhibited a photocurrent density of 4.1 mA/cm 2 at 1.23 V RHE under 1 sun AM 1.5G solar simulation and a low onset potential of 0.26 V RHE due to high majority carrier conductivity, a crystalline bulk with reduced defects as evidenced by x-ray photoelectron spectroscopy and photoluminescence lifetime analysis, and thus enhanced photocarrier collection. However, significant degradation in performance was found due to interfacial photocorrosion. To protect the surface and speed the oxygen-evolution reaction CoFeO x H y cocatalyst layers were deposited. By varying the number of consecutive sweeps and adjusting the applied bias range, an ultra-thin (~15 nm) CoFeO x H y cocatalyst layer was uniformly grown deposited over 30 cycles on the BiVO 4 surface. The resulting BiVO 4 /CoFeO x H y yielded 4.03 mA/cm 2 at 1.23 V RHE and onset potential of 0.24 V RHE , with stable operation (~15 % loss in photocurrent at 1.23 V RHE relative to ~60 % loss in the uncatalyzed control sample). These conformal CoFeO x H y catalytic layers function simultaneously to selectively collect photoexcited holes from the BiVO 4 , catalyze the water-oxidation reaction, and protect the BiVO 4 from photodegradation.
42 ENGINEERING↗
Learning control for slewing of a flexible panel
This paper studies the applicability of a discrete-time learning control method to the slewing control of a large flexible panel. Among the issues discussed are feasibility of the desired trajectories and their specification schemes, learning control by linear feedback, limitation of the actuator device output, and robustness to parameter changes or modeling errors associated with the chosen learning control design. To demonstrate the effectiveness of learning control, the system is designed with a proportional controller of the base angle only. Then application of the learning control is shown to make the system learn quickly to achieve the desired slewing without residual vibration at the end of the maneuver. Simulation results are reported and discussed.
Phan, M.↗
Range optimization for a supersonic aircraft
Range optimal trajectories for an aircraft flying in the vertical plane are obtained from Pontryagin's Minimum Principle. Control variables are load factor n which appears nonlinearly in the equations of motion and throttle setting eta, which appears only linearly. Both controls are subject to fixed bounds, namely eta between values of 0 and 1 and absolute value of n not greater than n(max). Additionally, a dynamic pressure limit is imposed, which represents a first-order state-inequality constraint. For fixed flight time, fixed initial coordinates, and partially fixed final coordinates, the effect of the load factor limit absolute value of n not greater than n(max) is studied. Upon varying n(max), six different switching structures are obtained. All trajectories involve singular control along arcs with active dynamic pressure limit.
Seywald, Hans↗
Nonlinear state estimation and feedback control of nonlinear and bilinear distributed parameter systems
This paper presents a theory of nonlinear state observers for nonlinear and bilinear distributed parameter systems. Convergence results are proved for these observers. Linear feedback control derived from such state observers is applied to the distributed parameter system and conditions are presented for closed-loop stability. The emphasis is on finite dimensional state observers and controllers (which can be implemented with on-line computers) and conditions for their successful operation with infinite dimensional distributed parameter systems.
Balas, M. J.↗
Design and simulation of a descent controller for strategic four-dimensional aircraft navigation
A time-controlled navigation system applicable to the descent phase of flight for airline transport aircraft was developed and simulated. The design incorporates the linear discrete-time sampled-data version of the linearized continuous-time system describing the aircraft's aerodynamics. Using optimal linear quadratic control techniques, an optimal deterministic control regulator which is implementable on an airborne computer is designed. The navigation controller assists the pilot in complying with assigned times of arrival along a four-dimensional flight path in the presence of wind disturbances. The strategic air traffic control concept is also described, followed by the design of a strategic control descent path. A strategy for determining possible times of arrival at specified waypoints along the descent path and for generating the corresponding route-time profiles that are within the performance capabilities of the aircraft is presented. Using a mathematical model of the Boeing 707-320B aircraft along with a Boeing 707 cockpit simulator interfaced with an Adage AGT-30 digital computer, a real-time simulation of the complete aircraft aerodynamics was achieved. The strategic four-dimensional navigation controller for longitudinal dynamics was tested on the nonlinear aircraft model in the presence of 15, 30, and 45 knot head-winds. The results indicate that the controller preserved the desired accuracy and precision of a time-controlled aircraft navigation system.
Lax, F. M.↗