8,331 research outputs found
Geometric characterization on the solvability of regulator equations
The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained
Research on output feedback control
In designing fixed order compensators, an output feedback formulation has been adopted by suitably augmenting the system description to include the compensator states. However, the minimization of the performance index over the range of possible compensator descriptions was impeded due to the nonuniqueness of the compensator transfer function. A controller canonical form of the compensator was chosen to reduce the number of free parameters to its minimal number in the optimization. In the MIMO case, the controller form requires a prespecified set of ascending controllability indices. This constraint on the compensator structure is rather innocuous in relation to the increase in convergence rate of the optimization. Moreover, the controller form is easily relatable to a unique controller transfer function description. This structure of the compensator does not require penalizing the compensator states for a nonzero or coupled solution, a problem that occurs when following a standard output feedback synthesis formulation
Electronic skewing circuit monitors exact position of object underwater
Linear Variable Differential Transformer /LVDT/ electronic skewing circuit guides a long cylindrical capsule underwater into a larger tube so that it does not contact the tube wall. This device detects movement of the capsule from a reference point and provides a continuous signal that is monitored on an oscilloscope
Infinite horizon control and minimax observer design for linear DAEs
In this paper we construct an infinite horizon minimax state observer for a
linear stationary differential-algebraic equation (DAE) with uncertain but
bounded input and noisy output. We do not assume regularity or existence of a
(unique) solution for any initial state of the DAE. Our approach is based on a
generalization of Kalman's duality principle. The latter allows us to transform
minimax state estimation problem into a dual control problem for the adjoint
DAE: the state estimate in the original problem becomes the control input for
the dual problem and the cost function of the latter is, in fact, the
worst-case estimation error. Using geometric control theory, we construct an
optimal control in the feed-back form and represent it as an output of a stable
LTI system. The latter gives the minimax state estimator. In addition, we
obtain a solution of infinite-horizon linear quadratic optimal control problem
for DAEs.Comment: This is an extended version of the paper which is to appear in the
proceedings of the 52nd IEEE Conference on Decision and Control, Florence,
Italy, December 10-13, 201
Control Barrier Function Based Quadratic Programs for Safety Critical Systems
Safety critical systems involve the tight coupling between potentially
conflicting control objectives and safety constraints. As a means of creating a
formal framework for controlling systems of this form, and with a view toward
automotive applications, this paper develops a methodology that allows safety
conditions -- expressed as control barrier functions -- to be unified with
performance objectives -- expressed as control Lyapunov functions -- in the
context of real-time optimization-based controllers. Safety conditions are
specified in terms of forward invariance of a set, and are verified via two
novel generalizations of barrier functions; in each case, the existence of a
barrier function satisfying Lyapunov-like conditions implies forward invariance
of the set, and the relationship between these two classes of barrier functions
is characterized. In addition, each of these formulations yields a notion of
control barrier function (CBF), providing inequality constraints in the control
input that, when satisfied, again imply forward invariance of the set. Through
these constructions, CBFs can naturally be unified with control Lyapunov
functions (CLFs) in the context of a quadratic program (QP); this allows for
the achievement of control objectives (represented by CLFs) subject to
conditions on the admissible states of the system (represented by CBFs). The
mediation of safety and performance through a QP is demonstrated on adaptive
cruise control and lane keeping, two automotive control problems that present
both safety and performance considerations coupled with actuator bounds
Zero Dynamics for Port-Hamiltonian Systems
The zero dynamics of infinite-dimensional systems can be difficult to
characterize. The zero dynamics of boundary control systems are particularly
problematic. In this paper the zero dynamics of port-Hamiltonian systems are
studied. A complete characterization of the zero dynamics for a
port-Hamiltonian systems with invertible feedthrough as another
port-Hamiltonian system on the same state space is given. It is shown that the
zero dynamics for any port-Hamiltonian system with commensurate wave speeds are
well-defined, and are also a port-Hamiltonian system. Examples include wave
equations with uniform wave speed on a network. A constructive procedure for
calculation of the zero dynamics, that can be used for very large system order,
is provided.Comment: 17 page
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