Stochastic Linearization of Feedback Systems With Multivariate Nonlinearities and Systems With State-Multiplicative Noise
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Linear regulator systems design with piecewise constant feedback gains determined by convergent digital computational algorithm
Nonlinear differential equations describing stability of fast nuclear reactor with incore thermionic converters and reactivity feedback
Design procedures are developed to select both eigenvalues and eigenvectors to improve system robustness. A robustness metric based on the determinant of the normalized eigenvector matrix defined. It is shown that this metric significantly speeds up the convergence of robust eigenvector solutions close to the optimal. A procedure to blend multiple inputs to improve achievable system robustness in the lower dimensional pseudo control space has also been derived.
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Because application of conventional optimal linear regulator theory to flight controller design requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. Therefore, a stochastic linear model that was developed is presented which accounts for aircraft parameter and initial uncertainty, measurement noise, turbulence, pilot command and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.
It is known that an effective control system is the key condition for successful implementation of high-performance magnetic servo systems. Major issues to design such control systems are nonlinearity; unmodeled dynamics, such as secondary effects for copper resistance, stray fields, and saturation; and that disturbance rejection for the load effect reacts directly on the servo system without transmission elements. One typical approach to design control systems under these conditions is a special type of nonlinear feedback called gain scheduling. It accommodates linear regulators whose parameters are changed as a function of operating conditions in a preprogrammed way. In this paper, an on-line learning fuzzy control strategy is proposed. To inherit the wealth of linear control design, the relations between linear feedback and fuzzy logic controllers have been established. The exercise of engineering axioms of linear control design is thus transformed into tuning of appropriate fuzzy parameters. Furthermore, fuzzy logic control brings the domain of candidate control laws from linear into nonlinear, and brings new prospects into design of the local controllers. On the other hand, a self-learning scheme is utilized to automatically tune the fuzzy rule base. It is based on network learning infrastructure; statistical approximation to assign credit; animal learning method to update the reinforcement map with a fast learning rate; and temporal difference predictive scheme to optimize the control laws. Different from supervised and statistical unsupervised learning schemes, the proposed method learns on-line from past experience and information from the process and forms a rule base of an FLC system from randomly assigned initial control rules.
Matrix method for optimal feedback control of linear systems
Optimal constant output feedback gains for linear multivariable systems, noting control vector as time invariant function of output vector
Equations were developed which describe the closed loop feedback system operation of a proposed ultrasonic, dynamic, nonintrusive flowmeter whose design is based on a constant phase, voltage controlled frequency feedback concept. These equations are based on linear feedback system theory. The time constant of a low pass filter is taken into account. The equations show that the larger the open loop gain, the smaller the error due to fluctuations in the speed of sound and the smaller the effective time constant.
Two approaches for studying the pursuit-evasion problem between rotorcraft executing nap-of-the-earth flight are presented. The first of these employs a constant speed kinematic helicopter model, while the second approach uses a three degree of freedom point-mass model. The candidate solutions to the first differential game are generated by integrating the state-costate equations backward in time. The second problem employs feedback linearization to obtain guidance laws in nonlinear feedback form. Both approaches explicitly use the terrain profile data. Sample extremals are presented.
Multiple coordinated robot arms are modeled by considering the arms: (1) as closed kinematic chains, and (2) as a force constrained mechanical system working on the same object simultaneously. In both formulations a new dynamic control method is discussed. It is based on a feedback linearization and simultaneous output decoupling technique. Applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, by choosing a general output equation, researchers can superimpose the position and velocity error feedback with the force-torque error feedback in the task space simultaneously.
Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.
Helicopters operating in high threat areas have to fly close to the earth surface to minimize the risk of being detected by the adversaries. Techniques are presented for low altitude helicopter trajectory planning. These methods are based on optimal control theory and appear to be implementable onboard in realtime. Second order necessary conditions are obtained to provide a criterion for finding the optimal trajectory when more than one extremal passes through a given point. A second trajectory planning method incorporating a quadratic performance index is also discussed. Trajectory planning problem is formulated as a differential game. The objective is to synthesize optimal trajectories in the presence of an actively maneuvering adversary. Numerical methods for obtaining solutions to these problems are outlined. As an alternative to numerical method, feedback linearizing transformations are combined with the linear quadratic game results to synthesize explicit nonlinear feedback strategies for helicopter pursuit-evasion. Some of the trajectories generated from this research are evaluated on a six-degree-of-freedom helicopter simulation incorporating an advanced autopilot. The optimal trajectory planning methods presented are also useful for autonomous land vehicle guidance.
Adaptive control technology is developed for the inner-loop speed and steering control of the MAX Rover. MAX, a CMU developed rover, is a compact low-cost 4-wheel drive, 4-wheel steer (double Ackerman), high-clearance agile durable chassis, outfitted with sensors and electronics that make it ideally suited for supporting research relevant to intelligent teleoperation and as a low-cost autonomous robotic test bed and appliance. The design consists of a feedback linearization based controller with a proportional - integral (PI) feedback that is augmented by an online adaptive neural network. The adaptation law has guaranteed stability properties for safe operation. The control design is retrofit in nature so that it fits inside the outer-loop path planning algorithms. Successful hardware implementation of the controller is illustrated for several scenarios consisting of actuator failures and modeling errors in the nominal design.
Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.
Linear single loop sampled data time delay feedback systems stability analysis