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Design of an optimal preview controller for linear discrete-time descriptor noncausal multirate systems.

Cao M, Liao F - ScientificWorldJournal (2014)

Bottom Line: The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system.The stabilizability and detectability of the lifted single-rate system are discussed in detail.The optimal preview control design techniques are illustrated by simulation results for a simple example.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China ; School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.

ABSTRACT
The linear discrete-time descriptor noncausal multirate system is considered for the presentation of a new design approach for optimal preview control. First, according to the characteristics of causal controllability and causal observability, the descriptor noncausal system is constructed into a descriptor causal closed-loop system. Second, by using the characteristics of the causal system and elementary transformation, the descriptor causal closed-loop system is transformed into a normal system. Then, taking advantage of the discrete lifting technique, the normal multirate system is converted to a single-rate system. By making use of the standard preview control method, we construct the descriptor augmented error system. The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system. In addition, a new single-rate system is obtained, the optimal control law of which is given. Returning to the original system, the optimal preview controller for linear discrete-time descriptor noncausal multirate systems is derived. The stabilizability and detectability of the lifted single-rate system are discussed in detail. The optimal preview control design techniques are illustrated by simulation results for a simple example.

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Related in: MedlinePlus

The output response to step function.
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Related In: Results  -  Collection


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fig1: The output response to step function.

Mentions: By MATLAB simulation, the output response of the linear discrete-time descriptor noncausal multirate system (with preview action and no preview action) is shown in Figure 1. The error signals are shown in Figure 2. Note that the preview action significantly reduces the error. In particular, the error signal is asymptotically zero.


Design of an optimal preview controller for linear discrete-time descriptor noncausal multirate systems.

Cao M, Liao F - ScientificWorldJournal (2014)

The output response to step function.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3921960&req=5

fig1: The output response to step function.
Mentions: By MATLAB simulation, the output response of the linear discrete-time descriptor noncausal multirate system (with preview action and no preview action) is shown in Figure 1. The error signals are shown in Figure 2. Note that the preview action significantly reduces the error. In particular, the error signal is asymptotically zero.

Bottom Line: The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system.The stabilizability and detectability of the lifted single-rate system are discussed in detail.The optimal preview control design techniques are illustrated by simulation results for a simple example.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China ; School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.

ABSTRACT
The linear discrete-time descriptor noncausal multirate system is considered for the presentation of a new design approach for optimal preview control. First, according to the characteristics of causal controllability and causal observability, the descriptor noncausal system is constructed into a descriptor causal closed-loop system. Second, by using the characteristics of the causal system and elementary transformation, the descriptor causal closed-loop system is transformed into a normal system. Then, taking advantage of the discrete lifting technique, the normal multirate system is converted to a single-rate system. By making use of the standard preview control method, we construct the descriptor augmented error system. The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system. In addition, a new single-rate system is obtained, the optimal control law of which is given. Returning to the original system, the optimal preview controller for linear discrete-time descriptor noncausal multirate systems is derived. The stabilizability and detectability of the lifted single-rate system are discussed in detail. The optimal preview control design techniques are illustrated by simulation results for a simple example.

Show MeSH
Related in: MedlinePlus