Real-time Auto Tuning of a Closed Loop Second Order System with Internal Time Delay Using Pseudo Random Binary Sequences

In this paper, a simple yet robust closed-loop identification method based on step response is presented. By approximating the process response firstly using Laguerre series expansions, a high-order process transfer function can be obtained. Then, a linear two-step reduction technique is used to reduce the high-order process to a second-order plus time delay model based on the frequency response data. This method is robust to measurement noise and it also does not need any numerical technique or iterative optimization. Simulation examples show the effectiveness of the proposed method for different process models. Comparison of identification performance between different methods is also illustrated in this work.

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Three Degrees of Freedom Active Control of Pneumatic Vibration Isolation Table by Pneumatic and Time Delay Control Technique

Journal of Vibration and Acoustics ◽

10.1115/1.4001509 ◽

2010 ◽

Vol 132 (5) ◽

Cited By ~ 22

Author(s):

Yun-Ho Shin ◽

Kwang-Joon Kim ◽

Pyung-Hoon Chang ◽

Dong Ki Han

Keyword(s):

Time Delay ◽

Active Control ◽

Vibration Isolation ◽

Decomposition Analysis ◽

Second Order ◽

Pneumatic Actuator ◽

Control Technique ◽

Order System ◽

Time Delay Control ◽

Delay Control

Based on previous feasibility study on one degree of freedom (1DOF) pneumatic active control of pneumatic springs, this paper presents procedures and results of a more realistic 3DOF active control of a pneumatic vibration isolation table. The 3DOF motion of the pneumatic table, consisting of heaving, rolling, and pitching, is controlled directly by adjusting air pressure in four pneumatic cylinders in a dynamic manner with pneumatic valves, without any external actuator such as an electromagnet or voice coil. The time delay control, which is a software chosen in this study, together with the hardware, i.e., the pneumatic actuator, is shown to be very powerful in enhancing the performance of vibration isolation for ground excitation as well as in settling time reduction for payload excitation through simulations and measurements on the 3DOF motion control system. New key results found in the experimental approach are that the pneumatic actuator shows a dynamic behavior of a second-order system, instead of a first-order system, which has been used in existing literatures so far, and that just feed-forward control of the pneumatic actuator by the second-order model can compensate for the inherently slow response characteristics of the pneumatic actuator very successfully. Effectiveness of the proposed active pneumatic control technique in the multi-input and multi-output system is shown via singular value decomposition analysis on the transmissibility matrix. Promising future of the proposed control and performance analysis technique is further discussed based on the results in the case of payload excitations as well.

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Adaptive LMS Model-Following Control Applied Inside a Closed-Loop

Volume 1C: 16th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc97/vib-3783 ◽

1997 ◽

Author(s):

Bradley R. Smith ◽

H. H. Robertshaw

Keyword(s):

Feedback Loop ◽

Closed Loop ◽

Delay Line ◽

Second Order ◽

Order System ◽

Control Problems ◽

Model Following Control ◽

Model Following ◽

Adaptive Lms ◽

Unknown Solution

Abstract A Least Mean Squares (LMS)-style algorithm is derived for the feedback control problem. The algorithm allows a tap delay line within the closed loop to be used for control applications. This paper derives the algorithm and applies the algorithm to two simple control problems for which the solution is known and to one problem with an unknown solution. The first problem is a stable second-order system. The second problem is a unstable second-order system which is initially stabilized with the feedback loop. In both problems, the weights converge to the expected values. The stable problem is used again with an inaccurate model that has 50% more damping than the actual plant. The weights converge to a solution which increases the performance of the controller.

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Enhanced PID Controller for Non-Minimum Phase Second Order Plus Time Delay System

Chemical Product and Process Modeling ◽

10.1515/cppm-2018-0059 ◽

2019 ◽

Vol 14 (3) ◽

Cited By ~ 2

Author(s):

Purushottam Patil ◽

C. Sankar Rao

Keyword(s):

Time Delay ◽

Closed Loop ◽

Linear Equations ◽

Uncertain System ◽

Absolute Error ◽

Delay System ◽

Second Order ◽

Delay Systems ◽

Minimum Phase ◽

Point Tracking

Abstract A tuning method is developed for the stabilization of the non-minimum phase second order plus time delay systems. It is well known that the presence of positive zeros pose fundamental limitations on the achievable control performance. In the present method, the coefficients of corresponding powers of s, s2 and s3 in the numerator are equated to α, β and γ times those of the denominator of the closed-loop system. The method gives three simple linear equations to get the PID parameter. The optimal tuning parameters α, β and γ are estimated by minimizing the Integral Time weighted Absolute Error (ITAE) for servo problem using fminsearch MATLAB solver aimed at providing lower maximum sensitivity function and keeping in check with the stability. The performance under model uncertainty is also analysed considering perturbation in one model parameter at a time using Kharitonov’s theorem. The closed loop performance of the proposed method is compared with the methods reported in the literature. It is observed that the proposed method successfully stabilizes and improves the performance of the uncertain system under consideration. The simulation results of three case studies show that the proposed method provides enhanced performance for the set-point tracking and disturbance rejection with improved time domain specifications.

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Analytical Design of Enhanced Fractional Filter PID Controller for Improved Disturbance Rejection of Second Order Plus Time Delay Processes

Chemical Product and Process Modeling ◽

10.1515/cppm-2018-0012 ◽

2018 ◽

Vol 14 (1) ◽

Cited By ~ 3

Author(s):

R. Ranganayakulu ◽

G. Uday Bhaskar Babu ◽

A. Seshagiri Rao

Keyword(s):

Time Delay ◽

Conventional Method ◽

Disturbance Rejection ◽

Closed Loop ◽

Order Approximation ◽

Higher Order ◽

Second Order ◽

Internal Model Control ◽

Robust Performance ◽

Fractional Filter

Abstract In this article, a modified fractional internal model control (IMC) filter structure is proposed to design a fractional filter Proportional-Integral-Derivative (FFPID) controller for improved disturbance rejection of second order plus time delay (SOPTD) processes. The proposed method aims at improving the disturbance rejection of slow chemical processes as the tuning rules for such processes are limited. The present design also considers the higher order approximation for time delay as it gives improved response for higher order processes. There is an additional tuning parameter in the proposed IMC filter apart from the conventional IMC filter time constant, which is tuned according to the derived formula. The additional adjustable parameter achieves the disturbance rejection and the closed loop stability. The simulation results have been performed for the same degree of robustness (maximum sensitivity, Ms) for a fair comparison. The results show an improved disturbance rejection for lag dominant and delay significant SOPTD processes with the proposed controllers designed using higher order Pade’s approximation of time delay than the proposed method using first order approximation and the conventional method. The closed loop robust performance is observed for perturbations in the process parameters and the performance is also observed for noise in the measurement. The robust stability analysis is carried out using sensitivity functions. In addition, the Ms range is also identified over which the system gives robust performance for the controllers designed using higher order pade’s approximation of time delay compared to conventional method.

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Approximation Methods for FO-IMC Controllers for Time Delay Systems

E3S Web of Conferences ◽

10.1051/e3sconf/201911501003 ◽

2019 ◽

Vol 115 ◽

pp. 01003

Author(s):

Cristina I. Muresan ◽

Isabela R. Birs ◽

Ovidiu Prodan ◽

Ioan Nascu ◽

Robin De Keyser

Keyword(s):

Time Delay ◽

Fractional Order ◽

Approximation Method ◽

Closed Loop ◽

Internal Model Control ◽

Delay Systems ◽

Order System ◽

Test Cases ◽

Time Delay Systems ◽

Model Control

Fractional Order Internal Model Control (FO-IMC) is among the newest trends in extending fractional calculus to the integer order control. Approximation of the FO-IMC is one of the key problems. Apart from this, when dealing with time delay systems, the time delay needs also to be approximated. All these approximations can alter the closed loop performance of the controller. In this paper, FO-IMC controllers will be tested in terms of the approximation accuracy. The case study is a first order system with time delay. Several scenarios will be considered, aiming for a conclusion regarding the choice of the approximation method as a function of the process characteristics, closed loop performance and FO-IMC fractional order. To approximate the time delay, two extensively used techniques will be considered, such as the series and Pade approximations. These will be compared to a novel approximation technique. An analysis of the test cases presented show that the series approximation proves more suitable in a single scenario, whereas the novel approximation method produces better results for the rest of the test cases.

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PID Controller optimization using Metahuristic Controller with Different Nonlinearities

Turkish Journal of Computer and Mathematics Education (TURCOMAT) ◽

10.17762/turcomat.v12i2.1082 ◽

2021 ◽

Vol 12 (2) ◽

pp. 764-771

Author(s):

G. Sundari, Et. al.

Keyword(s):

Steady State ◽

Pid Controller ◽

Closed Loop ◽

Error Function ◽

Second Order ◽

Settling Time ◽

Order System ◽

Pid Controllers ◽

Dynamic Performances ◽

Conventional Methods

This paper mainly explains the application of Metaherustic controller for tuning the parameter of PID controller. The minimization of error function has been done by improving the static and dynamic performances of the system like steady state error, Peak Overshoot, and Settling Time. This could be possible by means of applying metaherustic controller like GA in tuning the PID controllers under different Nonlinearities. The main intention of this paper is to support the specifications of PID controller at various Nonlinearities such as sinusoidal and saw tooth noise. The projected scheme derives the wonderful closed-loop response of second order system and then, it provides the effectiveness of the proposed method compared to the conventional methods.

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