Eigenvalue Assignment for Control of Time-Delay Systems Via the Generalized Runge–Kutta Method

This paper presents an eigenvalue assignment method for the time-delay systems with feedback controllers. A new form of Runge–Kutta algorithm, generalized from the classical fourth-order Runge–Kutta method, is utilized to stabilize the linear delay differential equation (DDE) with a single delay. Pole placement of the DDEs is achieved by assigning the eigenvalue with maximal modulus of the Floquet transition matrix obtained via the generalized Runge–Kutta method (GRKM). The stabilization of the DDEs with feedback controllers is studied from the viewpoint of optimization, i.e., the DDEs are controlled through optimizing the feedback gain matrices with proper optimization techniques. Several numerical cases are provided to illustrate the feasibility of the proposed method for control of linear time-invariant delayed systems as well as periodic-coefficient ones. The proposed method is verified with high computational accuracy and efficiency through comparing with other methods such as the Lambert W function and the semidiscretization method (SDM).

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Discussion on: Positive Real Control for Uncertain Singular Time-delay Systems via Output Feedback Controllers

European Journal of Control ◽

10.3166/ejc.10.303-336 ◽

2004 ◽

Vol 10 (4) ◽

pp. 303-336

Author(s):

Madgi s Mahmoud

Keyword(s):

Time Delay ◽

Output Feedback ◽

Delay Systems ◽

Time Delay Systems ◽

Positive Real ◽

Feedback Controllers ◽

Singular Time

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Optimal tuning of PID controller in time delay system: a review on various optimization techniques

Chemical Product and Process Modeling ◽

10.1515/cppm-2020-2001 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Thomas George ◽

V. Ganesan

Keyword(s):

Time Delay ◽

Pid Control ◽

Pid Controller ◽

Optimization Techniques ◽

Operating Conditions ◽

Delay Systems ◽

Pid Controllers ◽

Time Delay Systems ◽

Process Industries ◽

First Order

AbstractThe processes which contain at least one pole at the origin are known as integrating systems. The process output varies continuously with time at certain speed when they are disturbed from the equilibrium operating point by any environment disturbance/change in input conditions and thus they are considered as non-self-regulating. In most occasions this phenomenon is very disadvantageous and dangerous. Therefore it is always a challenging task to efficient control such kind of processes. Depending upon the number of poles present at the origin and also on the location of other poles in transfer function different types of integrating systems exist. Stable first order plus time delay systems with an integrator (FOPTDI), unstable first order plus time delay systems with an integrator (UFOPTDI), pure integrating plus time delay (PIPTD) systems and double integrating plus time delay (DIPTD) systems are the classifications of integrating systems. By using a well-controlled positioning stage the advances in micro and nano metrology are inevitable in order satisfy the need to maintain the product quality of miniaturized components. As proportional-integral-derivative (PID) controllers are very simple to tune, easy to understand and robust in control they are widely implemented in many of the chemical process industries. In industries this PID control is the most common control algorithm used and also this has been universally accepted in industrial control. In a wide range of operating conditions the popularity of PID controllers can be attributed partly to their robust performance and partly to their functional simplicity which allows engineers to operate them in a simple, straight forward manner. One of the accepted control algorithms by the process industries is the PID control. However, in order to accomplish high precision positioning performance and to build a robust controller tuning of the key parameters in a PID controller is most inevitable. Therefore, for PID controllers many tuning methods are proposed. the main factors that lead to lifetime reduction in gain loss of PID parameters are described in This paper and also the main methods used for gain tuning based on optimization approach analysis is reviewed. The advantages and disadvantages of each one are outlined and some future directions for research are analyzed.

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