Supervisory Control of Dynamical Systems With Uncertain Time Delays

2009 ◽  
Author(s):  
Bo Song ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Supervisory Control ◽  
Time Delays ◽  
Linear Time ◽  
Theoretical Work ◽  
Linear Time Invariant ◽  
Uncertain Time ◽  
Linear Time Invariant System ◽  
Time Invariant

This paper presents a study of controlling dynamical systems with uncertain and varying time delays. We apply the supervisory control algorithm to handle uncertainties in time delay. The hysteretic switching rule selects control gains out of the set of pre-determined optimal feedback gains for certain time delays in a range with known lower and upper bounds. The criterion is to judge when the system stays stable for any gains being selected and has a smaller switching index when the uncertain time delay varies in a known interval. A linear time-invariant system is used as an example to demonstrate the theoretical work.

Supervisory Control of Dynamical Systems With Uncertain Time Delays

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Bo Song ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Supervisory Control ◽  
Time Delays ◽  
Control Algorithm ◽  
Control Design ◽  
Theoretical Work ◽  
Mapping Method ◽  
Upper And Lower Bounds ◽  
Uncertain Time

A study of controlling dynamical systems with uncertain and varying time delays is presented in this paper. The uncertain time delay is assumed to fall in a range with known upper and lower bounds. We apply the supervisory control algorithm to deal with uncertainties in the time delay. An index is defined for each of the predetermined controls for a discrete set of time delays sampled from the range. Based on this index, a hysteretic switching rule selects a control from the predetermined controls with optimal feedback gains. Each predetermined control must be stable for any time delay in the range. Two control design methods are discussed, namely, the mapping method and a higher order approach. Examples of linear systems are used to demonstrate the theoretical work.

Design of Multi-Stage Optimal Arbitrary Time-Delay Filter

2013 ◽  
Vol 397-400 ◽  
pp. 1510-1514 ◽  
Author(s):  
Ke Ping Liu ◽  
Jian Peng Zeng ◽  
Min Yang ◽  
Chang Hong Jiang
Keyword(s):  
Time Delay ◽  
Control Method ◽  
Linear Time ◽  
Residual Vibration ◽  
Arbitrary Time ◽  
Linear Time Invariant ◽  
Flexible System ◽  
Multi Stage ◽  
Linear Time Invariant System ◽  
Time Invariant

Input shaping is an effective method for suppressing residual vibration of flexible system. In this paper, the design processes of Zero Vibration (ZV), Zero Vibration and Derivative (ZVD) shapers are deduced. Based on the idea of the robustness input shaper, the Multi-stage Optimal Arbitrary Time-delay Filter (MOATF) is proposed. The proposed control method is implemented on the second-order linear time-invariant system. Simulation results show that the residual vibration can be reduced effectively and the proposed method have great robustness in system parameter uncertainty.

scholarly journals Zeros in linear systems with time delay in state

2009 ◽  
Vol 19 (4) ◽  
pp. 609-617 ◽  
Author(s):  
Jerzy Tokarzewski
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Linear Time ◽  
Zero Dynamics ◽  
State Delay ◽  
Linear Time Invariant ◽  
System Output ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Time Invariant System

Zeros in linear systems with time delay in stateThe concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank, the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and zero dynamics. General formulas for output-zeroing inputs and zero dynamics are provided.

Decentralized time-delay controller design for systems described by delay differential-algebraic equations

2021 ◽  
pp. 014233122110159
Author(s):  
H. Ersin Erol ◽  
Altuğ İftar
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Controller Design ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Design Algorithm ◽  
Linear Time Invariant ◽  
Delay Differential ◽  
Time Invariant

This paper presents a complete approach for designing stabilizing linear time-invariant decentralized finite-dimensional or retarded time-delay output feedback controllers for linear time-invariant systems of delay differential-algebraic equations. The proposed approach is based on the sequential design of the local controllers by using a centralized controller design algorithm. In this sequential design approach, the local controller to be designed at each step is determined depending on the mobility of the rightmost modes with respect to the controllers that have not yet been designed and closed with the system. Since no predefined sequence is followed, a sequence that can target the least effort and dimension for each agent can be aimed. Also, in the proposed approach, a base controller effort can be targeted for each control agent, so that the effort required to stabilize the system can be distributed among the local controllers. In the centralized controller design algorithm used for the design of each local controller, the parameters of the controllers are changed stepwise in a quasi-continuous way to shift the targeted rightmost modes towards the stable area. For a time-delay controller, the desired mode placement can be achieved by applying small changes stepwise to the elements of the matrices and the time-delays of the controller while time-delays remain always non-negative. The effect of small perturbations on the time-delays in the open-loop system or to be added by the controller to be designed is taken into account to ensure some degree of robustness against all possible perturbations on the delays. The effectiveness of the proposed design approach is demonstrated by a numerical example.

Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

2008 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Time Delay ◽  
Transfer Functions ◽  
Linear Time ◽  
Order System ◽  
Pid Controllers ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Plant Transfer ◽  
Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

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