Compensator Design for a MEMS Gyroscope With Quadratic Optimal Control

2010 ◽  
Author(s):  
Wei Cui ◽  
Wei Xue ◽  
Xiaolin Chen
Keyword(s):  
Dynamic Range ◽  
Linear Quadratic Regulator ◽  
Control Algorithms ◽  
System Response ◽  
Linear Quadratic ◽  
Control Effort ◽  
Mems Gyroscope ◽  
Compensator Design ◽  
Wide Range ◽  
Parameter Perturbations

A number of control algorithms have been reported to adopt force balancing scheme into MEMS vibratory gyroscope systems. In practice, however, many algorithms are difficult to implement with electronic circuits. This paper designs and analyzes a lead compensator for a MEMS gyroscope via the Linear Quadratic Regulator (LQR) technique. LQR optimizes and balances the control effort and system response swiftness. Simulation shows the gyroscope achieves high linearity, wide dynamic range, and high robustness to fabrication uncertainties with this efficient compensator design. The closed-loop scale factor uniformity error is 0.7% under ±10% parameter perturbations. The compensator designed in this paper exhibits comparable outstanding performance compared to other reported control algorithms. The method reported in this paper is proved to be effective and can be used in a wide range of applications.

Robust Compensator Control of a Non-Resonant MEMS Gyroscope With Linear Quadratic Regulator

2010 ◽  
Author(s):  
Wei Cui ◽  
Xiaolin Chen ◽  
Wei Xue
Keyword(s):  
Closed Loop ◽  
Linear Quadratic Regulator ◽  
Open Loop ◽  
High Order ◽  
Behavior Modeling ◽  
Linear Quadratic ◽  
Parameter Uncertainties ◽  
Control Effort ◽  
Wide Range ◽  
Sinusoidal Input

This paper presents a controller design for a four degrees-of-freedom (4-DOF) non-resonant gyroscope via the linear quadratic regulator (LQR) technique. Compared to conventional MEMS gyroscopes, non-resonant gyroscopes are less vulnerable to fabrication perturbations. However, closed-loop performance of non-resonant gyroscopes has not been investigated previously. The control of non-resonant gyroscopes involves consideration of high order systems. LQR, which achieves balances between a fast response and a low control effort, has proven to be effective for high order systems. Our simulation results show that the closed-loop 4-DOF non-resonant gyroscope presented in this paper is able to achieve faster response and higher robustness to parameter uncertainties than the open-loop device. Under the sinusoidal input, compared to an error of 11.06% for the open-loop system, the closed-loop scale factor uniformity error is reduced to 0.014% under ±10% parameter perturbations. The device performance is analyzed by the behavior modeling approach in CoventorWare. The results show that the closed-loop non-resonant gyroscope achieves better performance through the LQR. The method reported here is proven to be effective and can be used in a wide range of applications.

Robust stabilization control of a spatial inverted pendulum using integral sliding mode controller

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishan Chawla ◽  
Vikram Chopra ◽  
Ashish Singla
Keyword(s):  
Inverted Pendulum ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Linear Quadratic Regulator ◽  
Humanoid Robots ◽  
Sliding Mode Controller ◽  
Linear Quadratic ◽  
Integral Sliding Mode ◽  
Wide Range ◽  
Lqr Controller

AbstractFrom the last few decades, inverted pendulums have become a benchmark problem in dynamics and control theory. Due to their inherit nature of nonlinearity, instability and underactuation, these are widely used to verify and implement emerging control techniques. Moreover, the dynamics of inverted pendulum systems resemble many real-world systems such as segways, humanoid robots etc. In the literature, a wide range of controllers had been tested on this problem, out of which, the most robust being the sliding mode controller while the most optimal being the linear quadratic regulator (LQR) controller. The former has a problem of non-robust reachability phase while the later lacks the property of robustness. To address these issues in both the controllers, this paper presents the novel implementation of integral sliding mode controller (ISMC) for stabilization of a spatial inverted pendulum (SIP), also known as an x-y-z inverted pendulum. The structure has three control inputs and five controlled outputs. Mathematical modeling of the system is done using Euler Lagrange approach. ISMC has an advantage of eliminating non-robust reachability phase along with enhancing the robustness of the nominal controller (LQR Controller). To validate the robustness of ISMC to matched uncertainties, an input disturbance is added to the nonlinear model of the system. Simulation results on two different case studies demonstrate that the proposed controller is more robust as compared to conventional LQR controller. Furthermore, the problem of chattering in the controller is dealt by smoothening the controller inputs to the system with insignificant loss in robustness.

Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller

2018 ◽  
Vol 19 (3-4) ◽  
pp. 379-389 ◽  
Author(s):  
Ishan Chawla ◽  
Ashish Singla
Keyword(s):  
Fuzzy Inference System ◽  
Inverted Pendulum ◽  
Fuzzy Inference ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Inference System ◽  
Wide Range ◽  
Lqr Controller ◽  
Rotary Inverted Pendulum

AbstractFrom the last five decades, inverted pendulum (IP) has been considered as a benchmark problem in the control literature due to its inherit nature of instability, non-linearity and underactuation. Its applicability in wide range of practical systems, demands the need of a robust controller. It is found in the literature that wide range of controllers had been tested on this problem, out of which the most robust being sliding mode controller while the most optimal being linear quadratic regulator (LQR) controller. The former has a problem of discontinuity and chattering, while the latter lacks the property of robustness. To address the robustness issue in LQR controller, this paper proposes a novel robust LQR-based adaptive neural based fuzzy inference system controller, which is a hybrid of LQR and fuzzy inference system. The proposed controller is designed and implemented on rotary inverted pendulum. Further, to validate the robustness of proposed controller to parametric uncertainties, pendulum mass is varied. Simulation and experimental results show that as compared to LQR controller, the proposed controller is robust to variations in pendulum mass and has shown satisfactory performance.

Control of a thermoelastic beam using heat actuation

2016 ◽  
Vol 23 (20) ◽  
pp. 3309-3326 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Joshua K Moua ◽  
Joe G Olivares
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rectangular Cross Section ◽  
Linear Quadratic Regulator ◽  
Elastic Displacement ◽  
Thermoelastic Damping ◽  
Linear Quadratic ◽  
Partial Differential ◽  
Control Effort ◽  
Thermoelastic Beam

This paper explores the idea of using heat as an actuator to simultaneously control vibration and temperature of a thermoelastic beam. We first model the beam as a slender, uniform cantilever beam of rectangular cross-section subject to heat through heat patches on the lower and upper surfaces at some discrete spanwise locations. The governing equations of the model are two coupled partial differential equations: one governing the elastic bending displacement and one governing the two-dimensional heat conduction of the beam. Through a discretization, the partial differential equations are replaced by a set of ordinary differential equations in a compact state-space form. We show that the coupling is actually between elastic displacement and those components of temperature contributing to the thickness-wise gradient at the midplane. The linear quadratic regulator in conjunction with the Kalman–Bucy filter is used for the control design to simultaneously damp out the displacement and the gradient. In a numerical example, we show the presence of thermoelastic damping due to the coupling. We also show that the displacement and gradient can simultaneously be controlled by using displacement measurements only, and that for less control effort it is also necessary to include some temperature measurements in the feedback.

scholarly journals A Novel Concept for Guidance and Control of Spacecraft Orbital Maneuvers

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Matteo Dentis ◽  
Elisa Capello ◽  
Giorgio Guglieri
Keyword(s):  
Attitude Control ◽  
Linear Quadratic Regulator ◽  
Control Algorithms ◽  
Linear Quadratic ◽  
C Language ◽  
Orbital Maneuvers ◽  
Guidance And Control ◽  
Actuation System ◽  
Novel Concept ◽  
And Control

The purpose of this paper is the design of guidance and control algorithms for orbital space maneuvers. A 6-dof orbital simulator, based on Clohessy-Wiltshire-Hill equations, is developed in C language, considering cold gas reaction thrusters and reaction wheels as actuation system. The computational limitations of on-board computers are also included. A combination of guidance and control algorithms for an orbital maneuver is proposed: (i) a suitably designed Zero-Effort-Miss/Zero-Effort-Velocity (ZEM/ZEV) algorithm is adopted for the guidance and (ii) a linear quadratic regulator (LQR) is used for the attitude control. The proposed approach is verified for different cases, including external environment disturbances and errors on the actuation system.

LQG Vibration Control of Aircraft Panel Using Automated State Weighting Procedure

2005 ◽  
Author(s):  
T. C. Waite ◽  
Christopher E. Whitmer ◽  
Atul G. Kelkar
Keyword(s):  
Maximum Amplitude ◽  
Linear Quadratic Regulator ◽  
Initial Guess ◽  
Performance Comparison ◽  
System Response ◽  
Linear Quadratic ◽  
Cabin Noise ◽  
Automated Method ◽  
And Control ◽  
Error State

Optimal control theory has long been plagued by its inability to optimize the state and control weighting matrices specified in the LQR (Linear Quadratic Regulator) cost function. Although this control is optimal for a given set of user-defined state and control weighting matrices, the performance of the controller varies widely based on the selection of these weights. Engineers have been left with the task of choosing appropriate weighting sequences by iterating each weight until the controller performs to their satisfaction. This procedure gets increasingly more frustrating and time consuming as the size of the controller increases. The work in this paper outlines an effective strategy which reduces the engineer’s effort in finding these weights. It is shown that the introduction of an additional performance index along with the repeated perturbation of an initial guess quickly leads to a controller with excellent performance. Comparison of this automated method with a controller exhaustively designed using a standard selection method reveals a closed loop system response which has more energy reduction and more maximum amplitude reduction, all in a fraction of the time it takes to guess and check the weights. The controller will be applied to the model of an aircraft panel in an effort to reduce vibrations caused by wind. The goal is to achieve a reduction in cabin noise by controlling the vibration of such panels. The system identification procedure uses a modification of the SOCIT toolbox to achieve extremely accurate frequency domain system models. The model obtained using this method will then be used in the design and simulation of both the trial-and-error state weighted controller and the automated state weighted controller.

scholarly journals Active Vibration Control of the Sting Used in Wind Tunnel: Comparison of Three Control Algorithms

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xing Shen ◽  
Yuke Dai ◽  
Mingxuan Chen ◽  
Lei Zhang ◽  
Li Yu
Keyword(s):  
Optimal Control ◽  
Wind Tunnel ◽  
Vibration Control ◽  
Control Algorithm ◽  
Active Vibration Control ◽  
Linear Quadratic Regulator ◽  
Real Time Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Active Vibration

In wind tunnel tests, cantilever stings are often used as model-mount in order to reduce flow interference on experimental data. In this case, however, large-amplitude vibration and low-frequency vibration are easily produced on the system, which indicates the potential hazards of gaining inaccurate data and even damaging the structure. This paper details three algorithms, respectively, Classical PD Algorithm, Artificial Neural Network PID (NNPID), and Linear Quadratic Regulator (LQR) Optimal Control Algorithm, which can realize active vibration control of sting used in wind tunnel. The hardware platform of the first-order vibration damping system based on piezoelectric structure is set up and the real-time control software is designed to verify the feasibility and practicability of the algorithms. While the PD algorithm is the most common method in engineering, the results show that all the algorithms can achieve the purpose of over 80% reduction, and the last two algorithms perform even better. Besides, self-tuning is realized in NNPID, and with the help of the Observer/Kalman Filter Identification (OKID), LQR optimal control algorithm can make the control effort as small as possible. The paper proves the superiority of NNPID and LQR algorithms and can be an available reference for vibration control of wind tunnel system.

Mixed Skyhook and Power-Driven-Damper: A New Low-Jerk Semi-Active Suspension Control Based on Power Flow Analysis

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Yilun Liu ◽  
Lei Zuo
Keyword(s):  
Active Control ◽  
Power Flow ◽  
Flow Analysis ◽  
Linear Quadratic Regulator ◽  
Control Algorithms ◽  
Linear Quadratic ◽  
Active Suspensions ◽  
Switching Law ◽  
Suspension Control ◽  
Optimal Linear

In practice, semi-active suspensions provide better tradeoffs between performances and costs than passive or active damping. Many different semi-active control algorithms have been developed, including skyhook (SH), acceleration-driven-damper (ADD), power-driven-damper (PDD), mixed SH and ADD (SH-ADD), and others. Among them, it has been shown that the SH-ADD is quasi-optimal in reducing the sprung mass vibration. In this paper, we analyze the abilities of vehicular suspension components, the shock absorber and the spring, from the perspective of energy transfer between the sprung mass and the unsprung mass, and propose a new sprung mass control algorithm named mixed SH and PDD (SH-PDD). The proposed algorithm defines a switching law that is capable of mixing SH and PDD, and simultaneously carries their advantages to achieve a better suspension performance. As a result, the proposed SH-PDD is effective in reducing the sprung mass vibration across the whole frequency spectrum, similar to SH-ADD and much better than SH, PDD, and ADD, while eliminating the control chattering and high-jerk behaviors as occurred in SH-ADD. The superior characteristics of the SH-PDD are verified in numerical analysis as well as experiments. In addition, the proposed switching law is extended to mix other semi-active control algorithms such as the mixed hard damping and soft damping, and the mixed SH and clipped-optimal linear quadratic regulator (LQR).

scholarly journals A Review of Control Algorithm for Autonomous Guided Vehicle

2020 ◽  
Vol 20 (1) ◽  
pp. 552
Author(s):  
Faiza Gul
Keyword(s):  
System Integration ◽  
Neural Control ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Control Algorithms ◽  
Linear Quadratic ◽  
Advantages And Disadvantages ◽  
Autonomous Guided Vehicle ◽  
Back Stepping Control ◽  
Linear Nature

The autonomous guided vehicle is a efficient and<br />effective platform for control system. Their non-linear nature helps<br />in analysing the control algorithms more efficiently and effectively.<br />The main objective of path planning is to find the optimal and<br />shortest path avoiding the time complexity so environment can be<br />modelled completely for vehicle. The paper includes explanation<br />of different systems together with numerous algorithms have been<br />discussed with advantages and disadvantages for example: Fuzzy<br />control, Neural Control, Back-stepping control, Adaptive control,<br />Sliding mode control and PID control and linear quadratic regulator.<br />The conclusion includes the hybrid system integration based<br />on the advantages and disadvantages presented in this paper.

Pitch and Depth Control of Underwater Glider using LQG and LQR via Kalman Filter

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
B. Ullah ◽  
M. Ovinis ◽  
M.B. Baharom ◽  
S.S.A Ali ◽  
M.Y. Javaid
Keyword(s):  
Kalman Filter ◽  
Linear Quadratic Regulator ◽  
Good Control ◽  
External Noise ◽  
Control Surface ◽  
Underwater Glider ◽  
Linear Quadratic ◽  
Control Effort ◽  
Underwater Gliders ◽  
Depth Control

Underwater gliders are adversely affected by ocean currents because of their low speed, which is compounded by an inability to make quick corrective manoeuvres due to limited control surface and weak buoyancy driven propulsion system. In this paper, Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) robust controllers are presented for pitch and depth control of an underwater glider. The LQR and LQG robust control schemes are implemented using MATLAB/Simulink. A Kalman filter was designed to estimate the pitch of the glider. Based on the simulation results, both controllers are compared to show the robustness in the presence of noise. The LQG controller results shows good control effort in presence of external noise and the stability of the controller performance is guaranteed.

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