scholarly journals The usage of Lambert W function for identification and speed control of a DC motor

2019 ◽  
Vol 32 (4) ◽  
pp. 581-600
Author(s):  
Radmila Gerov ◽  
Zoran Jovanovic
Keyword(s):  
Closed Loop ◽  
Dc Motor ◽  
Pole Placement ◽  
Step Response ◽  
Lambert W Function ◽  
Placement Method ◽  
Speed Regulation ◽  
Measured Speed ◽  
Proportional Controller ◽  
Integral Gain

The paper proposes a new method of identifying the linear model of a DC motor. The parameter estimation is based on the closed-loop step response of the DC motor under a proportional controller. For the application of the method, a deliberate delay of the measured speed was introduced. The paper considers the speed regulation of the direct current motor with negligible inductance by applying 1-DOF and 2-DOF, proportional integral retarded controllers. The proportional and integral gain of the PI retarded controllers was received by using a pole placement method on the identified model. The Lambert W function was applied for the identification and in designing the controller with the purpose of finding the rightmost poles of the closed-loop as well as the boundary conditions for selecting the gain of the PI controller. The robustness of the calculated controllers was considered under the effect of an disturbance, uncertainty in each of the DC motor parameters as well as perturbations in time delay.

A Recursive Pole Placement Method for Large Flexible Structures

1990 ◽  
Vol 112 (3) ◽  
pp. 407-410 ◽  
Author(s):  
H. Baruh
Keyword(s):  
Closed Loop ◽  
Flexible Structures ◽  
Open Loop ◽  
Pole Placement ◽  
Matrix Perturbation ◽  
Placement Method ◽  
Matrix Perturbation Theory ◽  
The Difference ◽  
Vibrating Systems ◽  
Uncontrolled System

This paper presents a recursive method to accomplish pole placement for control of large-order vibrating systems. The pole placement is based on matrix perturbation theory, where the controls are considered as a perturbation on the uncontrolled system. The difference between the open-loop poles and the desired closed-loop poles is divided into regions small enough to maintain validity of the perturbation assumption. Control gains are then calculated in each region, resulting in a stepwise design.

Data-driven I-PD Gain Tuning using Closed-loop Step Response Data

2019 ◽  
Vol 139 (8) ◽  
pp. 882-888
Author(s):  
Shiro Masuda ◽  
Jongho Park ◽  
Yoshihiro Matsui
Keyword(s):  
Closed Loop ◽  
Data Driven ◽  
Step Response ◽  
Response Data

Design and application of an optimally tuned PID controller for DC motor speed regulation via a novel hybrid Lévy flight distribution and Nelder–Mead algorithm

2021 ◽  
pp. 014233122110196
Author(s):  
Davut Izci
Keyword(s):  
Pid Controller ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Absolute Error ◽  
Dc Motor ◽  
Cuckoo Search Algorithm ◽  
Lévy Flight ◽  
Motor Speed ◽  
Levy Flight ◽  
Speed Regulation

This paper deals with the design of an optimally performed proportional–integral–derivative (PID) controller utilized for speed control of a direct current (DC) motor. To do so, a novel hybrid algorithm was proposed which employs a recent metaheuristic approach, named Lévy flight distribution (LFD) algorithm, and a simplex search method known as Nelder–Mead (NM) algorithm. The proposed algorithm (LFDNM) combines both LFD and NM algorithms in such a way that the good explorative behaviour of LFD and excellent local search capability of NM help to form a novel hybridized version that is well balanced in terms of exploration and exploitation. The promise of the proposed structure was observed through employment of a DC motor with PID controller. Optimum values for PID gains were obtained with the aid of an integral of time multiplied absolute error objective function. To verify the effectiveness of the proposed algorithm, comparative simulations were carried out using cuckoo search algorithm, genetic algorithm and original LFD algorithm. The system behaviour was assessed through analysing the results for statistical and non-parametric tests, transient and frequency responses, robustness, load disturbance, energy and maximum control signals. The respective evaluations showed better performance of the proposed approach. In addition, the better performance of the proposed approach was also demonstrated through experimental verification. Further evaluation to demonstrate better capability was performed by comparing the LFDNM-based PID controller with other state-of-the-art algorithms-based PID controllers with the same system parameters, which have also confirmed the superiority of the proposed approach.

Analysis of Reset Control Systems Consisting of a FORE and Second-Order Loop1

2001 ◽  
Vol 123 (2) ◽  
pp. 279-283 ◽  
Author(s):  
Qian Chen ◽  
Yossi Chait ◽  
C. V. Hollot
Keyword(s):  
Control Systems ◽  
Closed Loop ◽  
Second Order ◽  
Step Response ◽  
Steady State Response ◽  
First Order ◽  
State Response ◽  
Loop Transfer Function ◽  
Performance Specifications ◽  
Reset Control

Reset controllers consist of two parts—a linear compensator and a reset element. The linear compensator is designed, in the usual ways, to meet all closed-loop performance specifications while relaxing the overshoot constraint. Then, the reset element is chosen to meet this remaining step-response specification. In this paper, we consider the case when such linear compensation results in a second-order (loop) transfer function and where a first-order reset element (FORE) is employed. We analyze the closed-loop reset control system addressing performance issues such as stability, steady-state response, and transient performance.

A Note on Pole Placement of Mechanical Systems

1991 ◽  
Vol 113 (3) ◽  
pp. 420-421 ◽  
Author(s):  
C. Minas ◽  
D. J. Inman
Keyword(s):  
Least Squares ◽  
Canonical Form ◽  
Output Feedback ◽  
Closed Loop ◽  
Weighted Least Squares ◽  
Mechanical Systems ◽  
Pole Placement ◽  
Feedback Gain ◽  
Closed Loop System ◽  
Feedback Method

An output feedback method is developed, that systematically places a desired number of poles of a closed-loop system at or near desired locations. The system is transformed to its equivalent controllable canonical form, where the output feedback gain matrix is calculated in a weighted least squares scheme, that minimizes the change of the remaining modes of the system. The advantage of this method over other pole placement routines is the fact that the influence on the remaining unplaced modes of the system is minimum, which is particularly important in preserving closed-loop stability.

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