Reverse Engineering the LQR Controller to Find Equivalence with PID Controller

Author(s):  
Ali Nasir
Author(s):  
Ibrahim K. Mohammed ◽  
Abdulla I. Abdulla

This research work presents an efficient hybrid control methodology through combining the traditional proportional-integral-derivative (PID) controller and linear quadratic regulator (LQR) optimal controlher. The proposed hybrid control approach is adopted to design three degree of freedom (3DOF) stabilizing system for helicopter. The gain parameters of the classic PID controller are determined using the elements of the LQR feedback gain matrix. The dynamic behaviour of the LQR based PID controller, is modeled and the formulated in state space form to enable utlizing state feedback controller technique. The performance of the proposed LQR based LQR controller is improved by using Genetic Algorithm optimization method which are adopted to obtain optimum values for LQR controller gain parameters. The LQR-PID hybrid controller is simulated using Matlab environment and its performance is evaluated based on rise time, settling time, overshoot and steady state error parameters to validate the proposed 3DOF helicopter balancing system. Based on GA tuning approach, the simulation results suggest that the hybrid LQR-PID controller can be effectively adopted to stabilize the 3DOF helicopter system.


Author(s):  
Jharna Majumdar ◽  
Sudip C Gupta ◽  
B Prassanna Prasath

A detailed approach for a linear Proportional-Integral-Derivative (PID) controller and a non-linear controller - Linear Quadratic Regulator (LQR) is discussed in this paper. By analyzing several mathematical designs for the Skid Steer Mobile Robot (SSMR), the controllers are implemented in an embedded microcontroller - Mbed LPC1768. To verify the controllers, MATLAB-Simulink is used for the simulation of both the controllers involving motors - Maxon RE40. This paper compares between PID and LQR controller along with the performance comparison between Homogenous and Non-Homogenous LQR controllers.


2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
G. Barbaraci ◽  
G. Virzi' Mariotti

The control systems applied on active magnetic bearing are several. A perfect levitation is characterized by maintaining the operating point condition that is characterized by the center of stator coincident with the geometric center of shaft. The first controller implemented for this purpose is PID controller that is characterized by an algorithm that leads the amplifier to produce control current until the operating point condition is not reached, this is obtained by an integration operator. The effect of an integrator is essential but not necessary for a centered levitation for example in the robust control characterized by a dynamic model depended on plant of system so that it depends on angular speed as LQR controller does. In LQR there is not integrator so there is not a perfectly centered section of shaft with center of stator. On contrary PID controller does not depend on angular speed and it can be easily implemented according some simple rules. Predictive control is another interesting controller characterized by a multiple controller operating in different condition in order to get the minimum of cost function, but also in this case the angular speed is introduce for the same reason discussed before.


Author(s):  
Amir Torabi ◽  
Amin Adine Ahari ◽  
Ali Karsaz ◽  
Seyyed Hossin Kazemi

This paper exhibits a comparative assessmentbased on time response specification performance between modern and classical controller for a pitch control system of an aircraft system. The dynamic modeling of pitch control system is considered on the design of an autopilot that controls the pitch angle It starts with a derivation of a suitable mathematical model to describe the dynamics of an aircraft. For getting close to actual conditionsthe white noise disturbance is applied to the system.In this paper it is assumed that the modelpitch control systemis not available. So using the identification system and Box-Jenkins model estimator we identify the pitch control system System’s identification is a procedure for accurately characterizing the dynamic response behavior of a complete aircraft, of a subsystem, or of an individual component from measureddata.To study the effectiveness of the controllers, the LQR Controller and PID Controller and fuzzy controller is developed for controlling the pitch angle of an aircraft system. Simulation results for the response of pitch controller are presented instep’s response. Finally, the performances of pitch control systems are investigated and analyzed based on common criteria of step’s response in order to identify which control strategy delivers better performance with respect to the desired pitch angle. It is found from simulation, that the fuzzy controller gives the best performance compared to PID and LQR controller.


2016 ◽  
Vol 14 (1) ◽  
pp. 35-47
Author(s):  
Ts. Slavov ◽  
J. Kralev ◽  
P. Petkov

Abstract In this paper the developed two-wheeled robot and cascade LQR controller, Kalman filters, PI and PID controllers are presented. The cascade LQR controller stabilizes the two-wheeled robot in upright position. The PID controller ensures good tracking of wheel position reference and the PI controller steers two-wheeled robot rotation around the vertical axis. A software in MATLAB®/Simulink environment intended for design and generation of control code which is embedded in a Texas Instruments Digital Signal Controller is developed. Simulation and experimental results of system performance are given that confirm the efficiency of the control system developed.


2008 ◽  
Vol 45 ◽  
pp. 161-176 ◽  
Author(s):  
Eduardo D. Sontag

This paper discusses a theoretical method for the “reverse engineering” of networks based solely on steady-state (and quasi-steady-state) data.


2019 ◽  
Vol 139 (4) ◽  
pp. 356-363
Author(s):  
Yoichiro Ashida ◽  
Shin Wakitani ◽  
Toru Yamamoto

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