The solution of transport equations results in functional differential equations with time-delays. This papers deals with the control of linear systems with lumped and distributed delays that represent a coupled syste...
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The solution of transport equations results in functional differential equations with time-delays. This papers deals with the control of linear systems with lumped and distributed delays that represent a coupled system of transport processes and ordinary differential equations. These time-delay systems can be viewed as modules over a ring of entire functions. It is shown that spectral controllability and freeness of the module over an associated ring are necessary and sufficient for the module to be free. Using a module basis, a flatness-based tracking controller is derived that is infinite-dimensional, in general, due to the distributed delays. However, no (explicit) predictions are required to assign a finite spectrum to the delay system. Two examples illustrate the results, one of which being a neutral type system.
Abstract Flatness based analysis and closed loop control design for networks of hyperbolic p.d.e.'s is considered. To this end a state space description is assigned to the flatness based parametrization of the inp...
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Abstract Flatness based analysis and closed loop control design for networks of hyperbolic p.d.e.'s is considered. To this end a state space description is assigned to the flatness based parametrization of the input trajectories. Stabilization of this system by state feedback is discussed. By means of a state transformation which directly follows from the parametrization of the trajectories of the state variables, this feedback can be given in the original coordinates.
Linear systems with lumped and distributed delays can be represented by modules over the ring of entire functions in Ĉ( s )[e – τs ]. While in the case of commensurate delays spectral controllability is sufficient f...
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Linear systems with lumped and distributed delays can be represented by modules over the ring of entire functions in Ĉ( s )[e – τs ]. While in the case of commensurate delays spectral controllability is sufficient for the existence of a basis of this module, in the incommensurate case addressed here additional conditions are required. Exploiting the relations between the (known) delay amplitudes a new module with favorable freeness properties can be defined. Based on that, necessary and sufficient conditions for the freeness of this module are presented. If these conditions are satisfied a basis can be used to derive a flatness-based tracking control without any explicit predictions. The approach is illustrated on a neutral system and on a system with distributed delays.
A method is presented that allows for the identification of parameters in systems described by linear partial differential equations with spatially dependent coefficients. The approach uses operational calculus to gen...
An algebraic approach to parameter identification for transmission lines using boundary measurements is suggested. The class of systems under consideration can be modelled by means of linear partial differential equat...
Abstract control of systems where the information between the controller, actuator, and sensor can be lost or delayed can be challenging with respect to stability and performance. One way to overcome the resulting pro...
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Abstract control of systems where the information between the controller, actuator, and sensor can be lost or delayed can be challenging with respect to stability and performance. One way to overcome the resulting problems is the use of prediction based compensation schemes. Instead of a single input, a sequence of (predicted) future controls is submitted and implemented at the actuator. If suitable, so-called prediction consistent compensation and control schemes, such as certain predictive control approaches, are used, stability of the closed loop in the presence of delays and packet losses can be guaranteed. In this paper, we show that control schemes employing prediction based delay compensation approaches do posses inherent robustness properties. Specifically, if the nominal closed loop system without delay compensation is ISS with respect to perturbation and measurement errors, then the closed loop system employing prediction based delay compensation techniques is robustly stable. We analyze the influence of the prediction horizon on the robustness gains and illustrate the results in simulation.
Invariant feedback design for nonlinear systems in state representation with Lie symmetries is considered. Existing results regarding invariant control design based on (differential) invariants of the admitted symmetr...
Invariant feedback design for nonlinear systems in state representation with Lie symmetries is considered. Existing results regarding invariant control design based on (differential) invariants of the admitted symmetry group via exact input-output linearization are extended to the backstepping algorithm for systems in feedback form. Based on invariant errors obtained by normalization an approach for the design of set-point invariant feedback is proposed. Its application is demonstrated using the control of a predator-prey bioreactor as an example.
For linear delay systems with incommensurate (lumped) delays necessary and sufficient conditions for the freeness of the system over the ring of entire functions in are given. In contrast to the commensurate case the ...
A flatness-based feed-forward control design approach for an open channel flow modelled by the shallow water equations is discussed. The control input consists of the adjustable height of opening of a delimiting sluic...
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ISBN:
(纸本)9781424477456
A flatness-based feed-forward control design approach for an open channel flow modelled by the shallow water equations is discussed. The control input consists of the adjustable height of opening of a delimiting sluice gate. In order to compute the trajectory of the control input, the physical boundaries containing the control input are neglected and the problem is reduced to an initial value problem w.r.t. the spatial coordinate. The solution to this problem can be obtained with the method of characteristics.
A flatness based feed-forward control design approach for an open channel flow modelled by the shallow water equations is discussed. The control input consists of the adjustable height of opening of a delimiting sluic...
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