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Model reference adaptive control is applied to linear time varying systems and to nonlinear systems amenable to virtual linearization. Asymptotic stability is guaranteed even if the perfect model following conditions do not hold, provided that some sufficient conditions are satisfied. Simulations show the scheme to be capable of effectively controlling certain nonlinear systems.
The problem of designing a linear controller for systems subject to inequality variance constraints is considered. A quadratic penalty function approach is used to yield a linear controller. Both the weights in the quadratic penalty function and the locations of sensors and actuators are selected by successive approximations to obtain an optimal design which satisfies the input/output variance constraints. The method is applied to NASA's 64 meter Hoop-Column Space Antenna for satellite communications. In addition the solution for the control law, the main feature of these results is the systematic determination of actuator design requirements which allow the given input/output performance constraints to be satisfied.
Asymptotic properties and simulation of adaptive stochastic control for linear systems
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (O.L.F.O.) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first order systems are presented.
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with uncertain or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (OLFO) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.
Control-theory design package aids design of linear-quadratic-Gaussian (LOG) controllers and optimal filters. It is applicable to systems that can be modeled by linear time-invariant differential or difference equations.
Linear optimal regulator theory is applied to a nonlinear simulation of a transport aircraft performing a helical landing approach. A closed form expression for the quasi-steady nominal flight path is presented along with the method for determining the corresponding constant nominal control inputs. The Jacobian matrices and the weighting matrices in the cost functional are time varying. A method of solving for the optimal feedback gains is reviewed. The control system is tested on several alternative landing approaches using both three and six degree flight path angles. On each landing approach, the aircraft was subjected to large random initial state errors and to randomly directed crosswinds. The system was also tested for sensitivity to changes in the parameters of the aircraft and of the atmosphere. Performance of the optimal controller on all the three degree approaches was very good, and the control system proved to be reasonably insensitive to parametric uncertainties.
The results are presented of a detailed study of the discrete control of linear distributed systems with specific application to the design of a practical controller for a plant representative of a telescope primary mirror for an orbiting astronomical observatory. The problem of controlling the distributed plant is treated by employing modal techniques to represent variations in the optical figure. Distortion of the mirror surface, which arises primarily from thermal gradients, is countered by actuators working against a backing structure to apply a corrective force distribution to the controlled surface. Each displacement actuator is in series with a spring attached to the mirror by means of a pad intentionally introduced to restrict the excitation of high-order modes. Control is exerted over a finite number of the most significant modes.
Optical stationary control of linear control system with state dependent Gaussian noise
Equivalence of several theoretical approaches discussed. Report comments on application of geometric control theory (GCT), resolved-acceleration control (RAC), operational-space control (OSC), and nonlinear-decoupling theory (NDT) to remote manipulator consisting of multiple rigid links. Principal concern, search for nonlinear feedback law making end effector behave, for purposes of control, as though its dynamics linear and decoupled.
The design of nonlinear controllers has relied on the use of detailed aerodynamic and engine models that must be associated with the control law in the flight system implementation. Many of these controllers have been applied to vehicle flightpath control problems and have attempted to combine both inner- and outer-loop control functions in a single controller. This paper presents an alternate approach to the design of outer-loop controllers. The approach simplifies the outer-loop design problem by separating the inner-loop (stabilization and control) from the outer-loop (guidance and navigation) functions. Linearizing transformations are applied using measurement feedback to eliminate the need for detailed aircraft models in outer-loop control applications. Also discussed is an implementation of the controller. This implementation was tested on a six-degree-of-freedom F-15 simulation and in flight on an F-15 aircraft. Proof of the concept is provided by flight test data which is presented and discussed.
Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.
A general result for the controllability of linear systems using positive controls was given by Saperstone and Yorke (1971). These results are applied to systems with nearly nonnegative matrices and a theorem is developed which delineates the geometry of the reachable set.
AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft.
Optimal control generated by Kalman filter and least mean-squared predictor for linear systems with time delay
MSFC has successfully employed the use of the Vibrational Control of Space Structures (VCOSS) Linear Momentum Exchange Devices (LMEDs), which was an outgrowth of the Air Force Wright Aeronautical Laboratory (AFWAL) program, in a distributed control experiment. The control experiment was conducted in MSFC's Ground Facility for Large Space Structures Control Verification (GF/LSSCV). The GF/LSSCV's test article was well suited for this experiment in that the LMED could be judiciously placed on the ASTROMAST. The LMED placements were such that vibrational mode information could be extracted from the accelerometers on the LMED. The LMED accelerometer information was processed by the control algorithms so that the LMED masses could be accelerated to produce forces which would dampen the vibrational modes of interest. Experimental results are presented showing the LMED's capabilities.
Reduction of order technique pertaining to plant and reference model in controller design for linear plants transfer functions with zeros and slowly varying parameters
This paper discusses the implementation of a globally stable nonlinear controller algorithm for the Real-Time Interferometer Control System Testbed (RICST) brassboard optical delay line (ODL) developed for the Interferometry Technology Program at the Jet Propulsion Laboratory. The control methodology essentially employs loop shaping to implement linear control laws. while utilizing nonlinear elements as means of ameliorating the effects of actuator saturation in its coarse, main, and vernier stages. The linear controllers were implemented as high-order digital filters and were designed using Bode integral techniques to determine the loop shape. The nonlinear techniques encompass the areas of exact linearization, anti-windup control, nonlinear rate limiting and modal control. Details of the design procedure are given as well as data from the actual mechanism.