New Stability Analysis and Design of Discrete Time Delay Control for Nonaffine Nonlinear Systems

2020 ◽  
Author(s):  
Suresh B. Reddy
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Time Delay Control ◽  
Uncertain Dynamics ◽  
Discrete Time Delay ◽  
Delay Control ◽  
Continuous Time Delay ◽  
Nonaffine Nonlinear Systems

Abstract Time Delay Control (TDC) for linear and nonlinear systems with uncertain dynamics has been widely discussed in the literature, as it has a very simple and compact form. It uses time-delayed signals for estimating unknown dynamics at an instant, and uses feedback linearization for cancellation of known and estimated unknown dynamics. While the original formulation and most of the analyses have been focused on the continuous version of the controller, its implementation is more natural in digital form. This paper extends the recently improved sufficient Bounded Input - Bounded Output (BIBO) stability conditions for continuous Time Delay Control of nonaffine nonlinear systems to discrete Time Delay Control, including simplified approximate conditions under various assumptions. Additionally. asymptotic stability is established for similar conditions. The derived conditions are contrasted with earlier results for continuous Time Delay Control. Examples are used to illustrate the differences in continuous and discrete TDC, related to performance as well as sufficient and actual conditions for stability.

Discrete-Time Approximation of Multivariable Continuous-Time Delay Systems

2015 ◽  
pp. 516-542 ◽  
Author(s):  
Bemri H'mida ◽  
Mezlini Sahbi ◽  
Soudani Dhaou
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Continuous Time ◽  
Computational Cost ◽  
Discrete Systems ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Sampled Data ◽  
Discrete Time Delay ◽  
Continuous Time Delay

Many works are related to the analysis and control of either continuous or else discrete time-delay systems. In general, discrete-time controls have become more and more preferable in engineering because of their easy implementation and simple computation. However, the available discretization approaches for the systems having time delays increase the system dimensions and have a high computational cost. The case studies in this chapter support the efficiency of the two methods. However, the discretization of continuous time-delay systems has not been sufficiently/extensively studied in many works. In this work, the authors present two methods of the effective discretization approach for the continuous-time systems with an input and output delays. Sampled-data time-delay systems with internal and external point delays are described by approximate discrete time-delay systems in the discrete domain. These approximate discrete systems allow the hybrid control of time-delay systems.

Analysis of Linear Time Invariant Systems With Time Delay

1992 ◽  
Vol 114 (4) ◽  
pp. 544-555 ◽  
Author(s):  
K. Youcef-Toumi ◽  
S. Reddy
Keyword(s):  
Time Delay ◽  
Continuous Time ◽  
Control Algorithm ◽  
Closed Loop ◽  
Linear Time ◽  
Necessary Condition ◽  
Closed Loop System ◽  
Time Delay Control ◽  
Delay Control ◽  
Continuous Time Delay

Time Delay Control has recently been suggested as an alternative scheme for control of systems with unknown dynamics and unpredictable disturbances. The proposed control algorithm does not require an explicit plant model nor does it depend on the estimation of specific plant parameters. Rather, it uses information in the recent past to directly estimate the unknown dynamics at any given instant, through time delay. In earlier papers, analysis and implementation of Time Delay Controller for nonlinear systems were discussed. This paper analyzes the continuous Time Delay Controller for a class of linear systems and presents necessary and sufficient conditions for control system stability. A necessary condition for stability is derived using the properties of linear time-delayed systems. This condition involves only a few of the system and controller parameters and facilitates design of the Time Delay Controller. It is proved that this necessary condition is also sufficient if the delay time is chosen to be infinitesimally small. The convergence of closed loop system error to zero for certain classes of inputs and disturbances when the system is stable is also established. It is also shown that certain approximations in the control algorithm and certain additional unmodeled dynamics render the closed loop system under continuous Time Delay Control to be not exponentially stable due to the controller poles on the imaginary axis at infinitely high frequencies. However, in digital implementation, all the signals are prefiltered by anti-aliasing filters prior to sampling. Hence, the highest frequency component is automatically limited and the issue of exponential instability is not encountered. A discussion is presented comparing Time Delay Control with Repetitive Control. It is indicated that the Time Delay Controller can perform the functions of a repetitive controller with the delay time replaced by the period of the reference input while the repetitive controller can perform the functions of Time Delay Controller for sufficiently small “period” for a certain class of linear systems. Furthermore, examples are included to illustrate the results.

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