Iterative solution of nonlinear optimal control problems.
Mathematical programming methods for solving nonlinear state-constrained discrete optimal control problems
DYNAMIC PROGRAMMING↗
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Experimental results in nonlinear compensation of a one degree-of-freedom magnetic suspension
Nonlinear control techniques are of increasing interest in magnetic bearing applications. A one-degree-of-freedom magnetic suspension system has been constructed to serve as a test system for nonlinear control. The objective of this effort is to build an accurate model for the nonlinear suspension dynamics and to show the advantages of compensating for these nonlinearities by using a nonlinear controller. The results obtained with a nonlinear controller are experimentally demonstrated as superior to those obtained with a linear controller. Specifically, a controller which contains a force-control block yields transient responses which are largely independent of the operating point air gap.
Trumper, David L.↗
Forward Stochastic Nonlinear Adaptive Control Method
New method of computation for optimal stochastic nonlinear and adaptive control undergoing development. Solves systematically stochastic dynamic programming equations forward in time, using nested-stochastic-approximation technique. Main advantage, simplicity of programming and reduced complexity with clear performance/computation trade-offs.
Bayard, David S.↗
Stability of nonlinear attitude control systems, including particularly effect of large deflection of space vehicles.
Stability of nonlinear attitude control system coupled to flexible spacecraft under large deflection
Yu, Y.-Y.↗
Nonlinear lift control at high speed and high angle of attack using vortex flow technology
Nonlinear lift control at subsonic, transonic and low supersonic speeds owes its origin to the separated but organized vortical flows interacting with the wing upper surface. Since most of this flow originates near the wing or control-surface leading-edge, a variety of devices have been studied experimentally which interact with and/or control this flow in order to gain a beneficial effect. The benefits (effects) originally studied were only associated with lift enhancement. Whereas, now the studied benefits encompass performance increase, attention to changes in trimmed conditions and longitudinal stability, improvements in lateral stability, and the attendant variation with changing Mach number. For those devices that can be theoretically modeled, state-of-the-art computer codes have been used for device design and/or analysis. Comparisons at design and off-design conditions are presented for validation purposes.
Lamar, J. E.↗
A robust nonlinear attitude control law for space stations with flexible structural components
In this paper, a nonlinear attitude control law for space stations with flexible structural components is derived using a rigid-body model. This control law, depending on the Cayley-Rodriguez parameters, globally stabilizes the equilibrium of the rigid-body model. The effect of elastic deformations of the flexible structural components on the resulting feedback system dynamics is analyzed. It is found that the system's stability property is highly robust with respect to structural vibrations and inertial variations. The time-domain behavior of the feedback system is studied numerically using a model of a typical space station with flexible solar panels.
Wang, P. K. C.↗
Nonlinear lift control at high speed and high angle of attack using vortex flow technology
Nonlinear lift control at subsonic, transonic and low supersonic speeds owes its origin to the separated but organized vortical flows interacting with the wing upper surface. Since most of this flow originates near the wing or control-surface leading edge, a variety of devices has been studied experimentally which interact with and/or control this flow in order to gain a beneficial effect. The benefits (effects) originally studied were associated only with lift enhancement. Whereas, now the studied benefits encompass performance increase, attention to changes in trimmed conditions and longitudinal stability, improvements in lateral stability, and the attendant variation with changing Mach number. For those devices that can be theoretically modeled, state-of-the-art computer codes have been used for device design and/or analysis. Comparisons at design and off-design conditions are presented for validation purposes.
Lamar, John E.↗
Variable structure control of nonlinear systems through simplified uncertain models
A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.
Sira-Ramirez, Hebertt↗
Jump resonant frequency islands in nonlinear feedback control systems
A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.
Koenigsberg, W. D.↗
Alternatives for jet engine control
Nonlinear modeling researches involving the use of tensor analysis are presented. Progress was achieved by extending the studies to a controlled equation and by considering more complex situations. Included in the report are calculations illustrating the modeling methodology for cases in which variables take values in real spaces of dimension up to three, and in which the degree of tensor term retention is as high as three.
Sain, M. K.↗
Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization
This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.
Krishnan, Hariharan↗
A New Class of Nonlinear PID Controllers for Robotic Applications
This paper introduces a new class of simple nonlinear PID-type controllers comprised of a sector-bounded nonlinear gain in cascade with a linear fixed-gain P, PD, PI, or PID controller.
Robotic Applications PID Controllers Nonelinear ga↗
Effect of motor dynamics on nonlinear feedback robot arm control
A nonlinear feedback robot controller that incorporates the robot manipulator dynamics and the robot joint motor dynamics is proposed. The manipulator dynamics and the motor dynamics are coupled to obtain a third-order-dynamic model, and differential geometric control theory is applied to produce a linearized and decoupled robot controller. The derived robot controller operates in the robot task space, thus eliminating the need for decomposition of motion commands into robot joint space commands. Computer simulations are performed to verify the feasibility of the proposed robot controller. The controller is further experimentally evaluated on the PUMA 560 robot arm. The experiments show that the proposed controller produces good trajectory tracking performances and is robust in the presence of model inaccuracies. Compared with a nonlinear feedback robot controller based on the manipulator dynamics only, the proposed robot controller yields conspicuously improved performance.
Tarn, Tzyh-Jong↗
Controllability for linear and nonlinear systems
Controllability for linear and nonlinear systems
NONLINEAR SYSTEM↗
Divertor-safe nonlinear burn control based on a SOLPS parameterized core-edge model for ITER
Abstract For ITER operations, the range of desirable burning-plasma regimes with high fusion power output will be restricted by various operational constraints. These constraints include the saturation of ITER’s various heating and fueling actuators such as the neutral beam injectors, the ion and electron cyclotron heating systems, the gas puffing system, and the deuterium–tritium pellet injectors. In addition to these actuator constraints, the H-mode power threshold, divertor detachment, and the heat load on the divertor targets may apply limitations to ITER’s operational space. In this work, Plasma Operation Contour (POPCON) plots that map the aforementioned constraints to the temperature-density space are used to investigate which constraints are most limiting towards accessing regimes with high fusion power output. The presented POPCON plots are based on a control-oriented core-edge model that couples the nonlinear density and energy response models for the core-plasma region with SOLPS4.3 parameterizations for conditions in the edge-plasma regions (scrape-off-layer and divertor). Using this control-oriented core-edge model, a nonlinear burn controller, which aims to regulate the plasma temperature and density in the core-plasma region, is constructed in this work. This controller is augmented with an online optimization scheme that governs the control references such that the plasma can be guided towards regimes with high fusion powers while protecting the divertor targets from dangerously high heat loads. A closed-loop simulation study illustrates the capability of this burn control scheme.
Physics↗
Nonlinear adaptive control of an elastic robotic arm
An approach to control of a class of nonlinear flexible robotic systems is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. An adaptive torquer control law is derived for controlling the joint angles. This controller includes a dynamic system in the feedback path, requires only joint angle and rate for feedback, and asymptotically decomposes the elastic dynamics into two subsystems representing the transverse vibrations of the elastic link in two orthogonal planes. To damp out the elastic vibration, a force control law using modal feedback is synthesized. The combination of the torque and force control laws accomplishes joint angle control and elastic mode stabilization.
Singh, S. N.↗
Nonlinear Predictive Control of an Industrial Selective Catalytic Reduction Unit
Hedrick, E., K. Reynolds, D. Bhattacharyya, S.E. Zitney, and B. Omell, "Nonlinear Predictive Control of an Industrial Selective Catalytic Reduction Unit with Time-Varying Time Delay," AIChE 2021 Annual Meeting, Boston, MA, November 7-11 (2021).
Hedrick, Elijah↗
Viewing hybrid systems as products of control systems and automata
The purpose of this note is to show how hybrid systems may be modeled as products of nonlinear control systems and finite state automata. By a hybrid system, we mean a network of consisting of continuous, nonlinear control system connected to discrete, finite state automata. Our point of view is that the automata switches between the control systems, and that this switching is a function of the discrete input symbols or letters that it receives. We show how a nonlinear control system may be viewed as a pair consisting of a bialgebra of operators coding the dynamics, and an algebra of observations coding the state space. We also show that a finite automata has a similar representation. A hybrid system is then modeled by taking suitable products of the bialgebras coding the dynamics and the observation algebras coding the state spaces.
Grossman, R. L.↗