LQR

In this work, the active vibration control of a uniform cantilever beam using piezoelectric materials subjected to transverse vibrations is studied. The equation of motion of a beam bonded with the piezoelectric actuator is realized based on the Euler Bernoulli beam theory and the Hamilton's principle. A linear time invariant state space model is derived. Numerical simulations of the equation of motion are performed. Moreover, a finite element model of the beam-piezo system is done using ANSYS APDL©. Two control algorithms were also implemented using ANSYS APDL code to reduce the flapwise bending vibrations of the beam. The two control techniques are: Linear quadratic regulator (LQR) and positive-position-feedback (PPF). Results of the PPF simulations were compared with that of the LQR control and the advantage of using PPF control over LQR control in the finite element simulations is presented.

In this paper, the derivation of dynamic model of a robot arm on a two wheeled moving platform, and design of controllers to stabilize the robot arm are presented. The modeling of two wheeled moving platform is conducted through Simmechanics® toolbox of Matlab® software. Considered control approaches are PID control and linear quadratic gaussian (LGQ) for the dynamic system. The controllers are designed by using linearized model devised from Simmechanics®. Simulation studies are discussed. Control approaches are compared in detail in terms of tracking precision, quality of control signal. The aims of this study are derivation of linearized model for designing controllers, and determining the most appropriate controller for the real time system.

In this project a remote controlled self-balancing mobile robot was designed, built and controlled. This paper gives a summary of the work done in the fields of mechanical design, electronics, software design, system characterization and control theory. This wide array of fields necessary for the realization of the project holds the project up as a leading example in the field of mechatronics. In the paper special focus will be on the modelling of the robotic system and the simulation results of various control methods required for the stabilization of the system.

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.

This work presents a comparative study of two different control strategies for a flexible single-link manipulator. The dynamic model of the flexible manipulator involves modeling the rotational base and the flexible link as rigid bodies using the Euler Lagrange's method. The resulting system has one Degree-Of-Freedom (one DOF) and it provide freedom to increase the degree as well. Two types of regulators are studied, the State-Regulator using Pole Placement, and the Linear-Quadratic regulator (LQR). The LQR is obtained by resolving the Ricatti equation, in this work, we apply and compare two strategies to control the tip of the flexible link: state-feedback and linear quadratic regulator. These regulators are designed to reduce tip vibrations and increase system stability due to the flexibility of the arm.

In this report a number of algorithms for optimal control of a double inverted pendulum on a cart (DIPC) are investigated and compared. Modeling is based on Euler-Lagrange equations derived by specifying a Lagrangian, dierence between kinetic and potential energy of the DIPC system. This results in a system of nonlinear dieren tial equations consisting of three 2-nd order equations. This system of equations is then transformed into a usual form of six 1-st order ordinary dieren tial equations (ODE) for control design pur- poses. Control of a DIPC poses a certain challenge, since unlike a robot, the system is underactuated: one controlling force per three degrees of freedom (DOF). In this report, problem of optimal control minimizing a quadratic cost functional is addressed. Several approaches are tested: linear quadratic regulator (LQR), state-dependent Riccati equation (SDRE), optimal neural network (NN) control, and combinations of the NN with the LQR and the SDRE. Simulations rev...

This paper contains, performance of fuzzy controllers which evaluated and compared. It also describes the speed control based on Linear Quadratic Regulator (LQR) technique. The comparison is based on their ability of controlling the speed of DC motor, which merely focuses on performance of the controllers, and also time domain specifications such as rise time, settling time and peak overshoot. The controller is designed using MATLAB software, the results shows that the fuzzy controllers are the good but it as higher overshoot in comparison with optimal LQR. Thus, the comparative study recommends LQR controller gives better performance than the other controllers.

The optimal guidance law of an autonomous four-rotor helicopter, called the Quadrotor, using linear quadratic regulators (LQR) is presented in this paper. The dynamic equations of the Quadrotor are considered nonlinear so to find an LQR controller, it is necessary that these equations be linearized in different operation points. Due to importance of energy consumption in Quadrotors, minimum energy is selected as the optimal criteria

The aim of this study is to design a control strategy for the angular rate (speed) of a DC motor by varying the terminal voltage. This paper describes various designs for the control of direct current (DC) motors. We derive a transfer function for the system and connect it to a controller as feedback, taking the applied voltage as the system input and the angular velocity as the output. Different strategies combining proportional, integral, and derivative controllers along with phase lag compensators and lead integral compensators are investigated alongside the linear quadratic regulator. For each controller transfer function, the step response, root locus, and bode plot are analysed to ascertain the behaviour of the system, and the results are compared to identify the optimal strategy. It is found that the linear quadratic controller provides the best overall performance in terms of steady-state error, response time, and system stability. The purpose of the study that took place was to design the most appropriate controller for the steadiness of DC motors. Throughout this study, analytical means like tuning methods, loop control, and stability criteria were adopted. The reason for this was to suffice the preconditions and obligations. Furthermore, for the sake of verifying the legitimacy of the controller results, modelling by MATLAB and Simulink was practiced on every controller.

In this paper, a 3-axis motion simulator, as a three degree-of-freedom test stand for aircraft instrument testing and calibrating within a Hardware-In-The-Loop Environment, is studied for control analyses. A mathematical model of the simulator mechanical structure is derived and then linearized using Taylor series expansion around the instantaneous equilibrium point which is the aircraft time-dependant Euler angles and their rates. Also, the aircraft, earth and atmosphere are modeled in Matlab using Aerosim blocksets. A linear quadratic regulator (LQR) control law is developed to track the attitude, angular rates and angular acceleration of the Navion aircraft in a complicated maneuver. The control law is shown to be efficient in the presence of atmospheric turbulence, and robust to unknown bounded disturbances. The accuracy and correctness of the proposed control system is verified by the simulation.

This paper describes comparative study of various controllers on Rotary Inverted Pendulum (RIP). PID,
LQR, FUZZY LOGIC and H∞ controllers are tried on RIP in MatLab Simulink. The same four controllers
have been tested on test bed of RIP system the controllers are compared from various aspects. The
controllers in simulink are compared with the controllers in real time.

Linear quadratic regulation (LQR) has been treated as one of the most popular control strategies of a control system. Technically, this control methodology is based upon solving a special equation named Riccati algebraic equation to determine a decision vector, then to design the full state feedback control law. In such a control strategy, it is indispensable to decide two weighting matrices Q and R which can strongly affect the control performances of a system under consideration. This paper proposes a novel method to optimally determine the values for all elements of the matrices Q and R. This is executed by means of an efficient bio-inspired optimization mechanism. Whenever the two matrices Q and R are updated following the optimization technique, the state vector will be improved and a fitness or cost function is always evaluated to optimize the control performance of the system. The proposed control strategy will also be demonstrated through a typical case study of load-frequency control problem of a thermal power plant. A significant number of numerical simulation results will be provided to testify the feasibility and superiority of the power system applying the LQR scheme proposed in this study over the conventional PID regulators.

For multiple input-multiple output (MIMO) systems, the most common control strategy is the linear quadratic regulator (LQR) which relies on state vector feedback. Despite this strategy gives very good result, it still has trial and error procedure to select the values of its weight matrices which plays a important role in reaching to the desiered system performance. In order to overcome this problem, the Genetic algorithm is used. The design of genetic algorithm based linear quadratic regulator (GA-LQR) utilized Integral time absolute error (ITAE) as a cost function for optimization. The propsed procedure is implemented on a linear model of gas turbine to control the generator spool's speed and the output power.

It is well known that for computer simulation and analysis of power systems both planning and operation are necessary. Computer simulation requires an appropriate mathematical model that many inter-related linear, nonlinear, differential and algebraic equations of the system. Such mathematical model is needed for analysis and improves power system dynamic stability performance and also design a suitable controller. This paper provides comprehensive development procedure and final forms of mathematical models of a power system installed with UPFC and controller UPFC using linear quadratic regulator techniques for stability improvement. The impacts of control strategy on power system multi machine installed with UPFC, without UPFC and with controller UPFC at different loading and operating conditions are discussed. The accuracy of the developed models is verified through comparing the study results with those obtained from detailed MATLAB programming. In this paper settling time analysis also have been done for justification of the stability improvement.

ABSTRACT This paper presents an evolutionary optimization based LQR controller design for an inverted pendulum system. The objective is to address the challenges of appropriate design parameters selection in LQR controller while providing optimal performance compromise between the system control objectives with respect to pendulum angle and position response. Hence, a Multiobjective differential evolution algorithm is proposed to design an LQR controller with optimal compromise between the conflicting control objectives. The performance of the MODEbased LQR is benchmarked with an existing controller from the system manufacturer (QANSER). The performance shows the effectiveness of the proposed design algorithm, and in addition provides an efficient solution to conventional trial and error design approach.

Since the main structure of a self-balancing robot is nonlinear and complicated, it has always some uncertainties in it. Using ordinary optimal control approaches for solving these kinds of problems make an incorrect solution for that. In this research, a new technique is proposed to solve the optimal control of a self-balancing robot in the presence of interval uncertainties. The proposed method is constructed with an interval extension of the second kind Chebyshev polynomials. Because of the system uncertainties, the controllability of the system is first analyzed. Afterward, an interval based version of the linear quadratic regulator (LQR) is introduced to solve the interval Ricatti equations and to obtain proper confidence interval. Final results are compared with Monte Carlo method and the results demonstrate the effectiveness of the proposed method.

Abstract The main objective of this paper is to design a state feedback controller for stabilizing and tracking control of self-erecting inverted pendulum employing intelligent method using particle swarm optimization (PSO). This is motivated by the fact that one has to face trial and error approach in conventional feedback control design by pole placement method or linear quadratic regulator (LQR) method via Riccati equation. The simulation results show the effectiveness of the proposed method. The proposed state feedback ...

In this paper, the derivation of dynamic model of a robot arm on a two wheeled moving
platform, and design of controllers to stabilize the robot arm are presented. The modeling of two
wheeled moving platform is conducted through Simmechanics toolbox of Matlab software.
Considered control approaches are PID control and linear quadratic gaussian (LGQ) for the dynamic
system. The controllers are designed by using linearized model devised from Simmechanics.
Simulation studies are discussed. Control approaches are compared in detail in terms of tracking
precision, quality of control signal. The aims of this study are derivation of linearized model for
designing controllers, and determining the most appropriate controller for the real time system.

In this work a dynamic model of a new quadrotor aerial vehicle that is equipped with a tilt-wing mechanism is presented. The vehicle has the capabilities of vertical take-off/landing (VTOL) like a helicopter and flying horizontal like an airplane. Dynamic model of the vehicle is derived both for vertical and horizontal flight modes using Newton-Euler formulation. An LQR controller for the vertical flight mode has also been developed and its performance has been tested with several simulations. Keywords—Control, Dynamic model, LQR, Quadrotor, Tilt-wing, VTOL.

This paper presents an alternative approach for the model-based control of the ";ball and beam";, a multivariable nonlinear dynamic system, which is a benchmark for testing new control algorithms. The proposed strategy uses two neural networks and a polynomial interpolating scheme to construct the desired value trajectory. The performance of this strategy significantly outperforms the corresponding to the classic linear quadratic regulator. Both strategies were implemented on computer simulations of the system, and their performance was evaluated using the following criteria: rise time, settling time, overshoot percentage, integral of the error's absolute value, robustness and design easiness. The control strategies were tested under step and sinusoidal changes of the reference value.

The optimal guidance law of an autonomous four-rotor helicopter, called the Quadrotor, using linear quadratic regulators (LQR) is presented in this paper. The dynamic equations of the Quadrotor are considered nonlinear so to find an LQR controller, it is necessary that these equations be linearized in different operation points. Due to importance of energy consumption in Quadrotors, minimum energy is selected as the optimal criteria

A dc-dc zeta converter is a switch mode dc-dc converter that can either stepup or step-down dc input voltage. In order to regulate the dc output voltage, a control subsystem needs to be deployed for the dc-dc zeta converter. This paper presents the dc-dc zeta converter control. Unlike conventional dc-dc zeta converter control which produces a controller based on the nominal value model, we propose a convex polytope model of the dc-dc zeta converter which takes into account parameter uncertainty. A linear matrix inequality (LMI) is formulated based on the linear quadratic regulator (LQR) problem to find the state-feedback controller for the convex polytope model. Simulation results are presented to compare the control performance between the conventional LQR and the proposed LMI based controller on the dc-dc zeta converter. Furthermore, the reduction technique of the convex polytope is proposed and its effect is investigated.