Second Order Plus Time Delay Research Articles

A Simple Identification Technique for Second-Order plus Time-Delay Systems

Second-Order plus Time-Delay (SOPTD) models are commonly used to approximate systems in order to tune PID controllers. Simple models are dominating for control design in industrial applications. Several estimation techniques have been developed and applied to controller design. Most estimation techniques are based on least-squares and excitations such as step, square waves and pseudo-random signals. In order to speed up the experiments, simple and short excitations have also been considered. In this paper alternatives are proposed to robustify the estimates in order to obtain a better model around important frequencies. Simulation results are presented to illustrate the techniques.

Optimal tuning of PID controllers for FOPTD, SOPTD and SOPTD with lead processes

This paper presents the synthesis and analysis of optimal tuning of proportional integral derivative (PID) parameters for different process systems: first order plus time delay (FOPTD), second order plus time delay (SOPTD) and second order plus time delay with lead (SOPTDLD). This work involved optimization of the PID control parameters to achieve the minimization of the integral absolute error (IAE). A set of new and generalized tuning correlations relating the controller parameters to the process parameters was obtained for step changes in set point and load separately. Simulation results showed that the use of the proposed tuning correlations results in superior closed loop performance compared to other tuning techniques previously proposed in the literature.

A robust polynomial-based control for stable processes with time delay

In this paper, the coefficient diagram method (CDM) is used to design a controller for stable processes with a time delay to achieve high performance. For this, first order plus time delay (FOPTD) and second order plus time delay (SOPTD) models are used. The explicit tuning formulae of the controller using the polynomial representation are presented based on closed-loop pole-allocation strategy according to the FOPTD and SOPTD plant models. The results are compared with other commonly available tuning methods. It is shown that the CDM control system is more successful in view of the stability, time response, disturbance rejection and robustness properties of the closed loop system.

Direct Identification Method of Second Order Plus Time Delay Model Parameters

In this paper, we propose an identification method to estimate the second order plus time delay (SOPTD) model parameters. The proposed method directly obtains these parameters using a frequency-weighted integral transform and a least-squares method, without iterative calculation step. This calculation procedure can be applied regardless of initial states, in contrast to almost all previous identification methods, which require the assumption of zero initial states. In addition, it does not require any additional model reduction steps to tune the PID controller. Using simulations, it is demonstrated that the proposed method provides better modeling performance than previous methods, in spite of its simplicity. The new method shows an acceptable robustness to disturbance and measurement noise.

Closed-loop identification and control application for dissolved oxygen concentration in a full-scale coke wastewater treatment plant

The objective of this paper is to apply a closed-loop identification to actual dissolved oxygen control system in the coke wastewater treatment plant. It approximates the dissolved oxygen dynamics to a high order model using the integral transform method and reduces it to the first-order plus time delay (FOPTD) or second-order plus time delay (SOPTD) for the PID controller tuning. To experiment the process identification on the real plant, a simple set-point change of the speed of surface aerator under the closed-loop control without any mode change was used as an activation signal of the identification. The full-scale experimental results show a good identification performance and a good tracking ability for set-point change. As a result of improved control performance, the fluctuation of dissolved oxygen concentration variation has been decreased and the electric power saving has been accomplished.

An Enhanced Process Identification Method for Automatic Tuning of PID Controller

An enhanced process identification method with biased-relay feedback is proposed for the design of PID controller This paper suggested a new theorem to get the transfer function of a process from the definition of Laplace transformation without any approximation. Based on this theorem, the process is identified as the second-order plus time delay (SOPTD) model with a least-squares method in a viewpoint of amplitude ratio and phase angle between the process and the SOPTD model. Since the proposed identification method does not approximate the relay and process outputs as sinusoidal signals, then the obtained SOPTD model can represent the process dynamics more accurately. A simulation study demonstrates its effectiveness and robustness to the measurement noise.

Robust PID tuning for Smith predictor in the presence of model uncertainty

Abstract This paper presents robust PID tuning for the Smith predictor in the presence of model uncertainty. The concept of the equivalent gain plus time delay (EGPTD) is introduced to incorporate robust stability in PID tuning of the Smith predictor. In particular, an application is developed for the robust tuning of the first order plus time delay (FOPTD) system and the second order plus time delay (SOPTD) system because the systems have been used extensively to describe chemical processes. The proposed tuning method can cope with simultaneous uncertainties in all parameters of the model in an efficient manner. Another important and attractive feature of the method is that it can utilize many currently available PID tuning rules. Simulation results are provided to demonstrate the availability of the method.

A Direct Estimation Method of Second Order Plus Time Delay Model Parameters for PID Controller Autotuning.

In this paper, we propose an identification method to estimate the second order plus time delay (SOPTD) model parameters. The proposed method obtains the parameters of the SOPTD model directly using a time weighted integral transform and a least square method, so model reduction steps can be avoided to tune the PID controller. It can also be applied regardless of the initial states while almost all previous identification methods require the assumption of zero initial states. Through extensive simulations, it is proved clearly that the proposed method gives acceptable estimation performances whether initial states are zero or not. Moreover, it shows an acceptable robustness to the disturbances and measurement noise.

Closed-loop on-line process identification using a proportional controller

A new identification method using a proportional controller is proposed for autotic tuning of PID controller. A second-order plus time-delay (SOPTD) model is obtained by a least-squares method in the frequency domain. The suggested method can remove the restriction in applicability of previous methods so that it can be applied to any stable closed-loop response, regardless of the type of the transient such as overdamped, underdamped and inverse response. It is simple so that it does not need any complex techniques such as root finding or optimization method. With the obtained model parameters, the three parameters of PID controller can be calculated from the integral of the time-weighted absolute value of the error (ITAE) tuning rule on-line. Simulation study shows the robustness with respect to measurement noise and disturbance at the identification stage.