1,720,990 research outputs found
New formulae and graphics for compensator design
No full textIn this paper, two simple 'inversion formulae' for analytic design of lead and lag compensators are proposed, and a graphical interpretation for them is given. Their use in connection with both Bode and Nyquist diagrams is pointed out with some numerical examples
A Nested Computational Approach to the Discrete-Time Finite-Horizon LQ Control Problem
No full textA new algorithmic setting is proposed for the discrete-time finite-horizon linear quadratic (LQ) optimal control problem with constrained or unconstrained final state, no matter whether the problem is cheap, singular, or regular. The proposed solution, based on matrix pseudoinversion, is completed and made practically implementable by a nesting procedure for welding optimal subarcs that enables arbitrary enlargement of the control time interval
Convolution profiles for right inversion of multi-variable non-minimum phase discrete-time systems
No full textThe problem of the non-causal inversion of linear multivariable discrete-time systems is analyzed in the geometric approach framework and is solved through the computation of convolution profiles which guarantee perfect tracking under the assumption of infinite-length preaction and postaction time intervals. It is shown how the shape of the convolution profiles is related to both the relative degree and the invariant zeros of the plant. A computational setting for the convolution profiles is derived by means of the standard geometric approach tools. Feasibility constraints are also taken into account. A possible implementation scheme, based on a finite impulse response system acting on a stabilized control loop, is provided. © 2002 Elsevier Science Ltd. All rights reserved
Generalized signal decoupling problem with stability for discrete-time systems
No full textThis paper deals with the decoupling problems of unknown, measurable, and previewed signals. First, well-known solutions of unknown and measurable disturbance decoupling problems are recalled. Then, new necessary and sufficient constructive conditions for the previewed signal decoupling problem are proposed. The discrete-time case is considered. In this domain, previewing a signal by p steps means that the kth sample of the signal to be decoupled is known p steps in advance. The main result is that the stability condition for the mentioned decoupling problems does not change; i.e., the resolving subspace to be stabilized is the same independently of the type of signal to be decoupled, no matter whether it is completely unknown, measured, or previewed. The problem has been studied through self-bounded controlled invariants, thus minimizing the dimension of the resolving subspace which corresponds to the infimum of a lattice. The reduced dimension of the resolving controlled invariant subspace reduces the order of the controller units
Employing the algebraic Riccati equation for the solution of the finite-horizon LQ problem
No full text
A unified algorithmic setting for signal-decoupling compensators and unknown-input observers
No full textA standard geometric-type environment, where only the very basic tools of the geometric approach are used (those supported by well-settled and well-tested computational aids) enables the development of algorithms for numerous control and estimation problems in the discrete-time case. These are: measurable or previewed signal localization problems, perfect or almost perfect tracking (right inversion), and, by duality, perfect or almost perfect unknown input estimation with possible post-knowledge and input reconstruction (left inversion). It is also shown that the devices obtained (compensator and observer), that may be noncausal when specific stability requirements are not met, can be implemented as dynamical systems including finite-horizon convolutors or finite impulse response systems
Solving signal decoupling problems through self-bounded controlled invariants
No full textThis paper deals with decoupling problems of unknown, measurable and previewed signals. First the well known solutions of unknown and measurable disturbance decoupling problems are recalled. Then new necessary and sufficient constructive conditions for the previewed signal decoupling problem are proposed. The discrete time case is considered. In this domain previewing a signal by p steps means that the k-th sample of the signal to be decoupled is known p steps in advance. The main result is to prove that the stability condition for all of the mentioned decoupling problems does not change, i.e. the resolving subspace to be stabilized is the same independently of the type of signal to be decoupled, being it completely unknown (disturbance), measured or previewed. The problem has been studied through self-bounded controlled invariants, thus minimizing the dimension of the resolving subspace which corresponds to the infimum of a lattice. Note that reduced dimension on resolving controlled invariant subspace yields to reduce the order of the controller units
Geometric insight into discrete-time cheap and singular linear quadratic Riccati (LQR) problems
No full textThe Hamiltonian system related to discrete-time cheap linear quadratic Riccati (LQR) problems is analyzed in a purely geometric context, with the twofold purpose of getting a useful insight into its structural features and deriving a numerically implementable solution for the infinite-horizon case by only using the standard geometric approach routines available
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