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.

Hovering stability of a model helicopter

2016 ◽  
Vol 88 (6) ◽  
pp. 810-817 ◽  
Author(s):  
Ilker Murat Koc ◽  
Semuel Franko ◽  
Can Ozsoy
Keyword(s):  
Initial Conditions ◽  
Linear Quadratic Regulator ◽  
Open Loop ◽  
Small Scale ◽  
Linear Quadratic ◽  
Parameter Uncertainties ◽  
Control Effort ◽  
Content Type ◽  
Modeling Uncertainties ◽  
Angular Displacements

Purpose The purpose of this paper is to investigate the stability of a small scale six-degree-of-freedom nonlinear helicopter model at translator velocities and angular displacements while it is transiting to hover with different initial conditions. Design/methodology/approach In this study, model predictive controller and linear quadratic regulator are designed and compared within each other for the stabilization of the open loop unstable nonlinear helicopter model. Findings This study shows that the helicopter is able to reach to the desired target with good robustness, low control effort and small steady-state error under disturbances such as parameter uncertainties, mistuned controller. Originality/value The purpose of using model predictive control for three axes of the autopilot is to decrease the control effort and to make the close-loop system insensitive against modeling uncertainties.

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.

Optimal attitude trajectory planning method for CMG actuated spacecraft

2017 ◽  
Vol 232 (1) ◽  
pp. 131-142 ◽  
Author(s):  
Lijun Zhang ◽  
Chunmei Yu ◽  
Shifeng Zhang ◽  
Hong Cai
Keyword(s):  
Trajectory Planning ◽  
Closed Loop ◽  
Pseudospectral Method ◽  
Linear Quadratic Regulator ◽  
Fixed Time ◽  
Open Loop ◽  
Planning Method ◽  
Global Perspective ◽  
Linear Quadratic ◽  
Loop Control

This paper presents an optimal attitude trajectory planning method for the spacecraft equipped with control moment gyros as the actuators. Both the fixed-time energy-optimal and synthesis performance optimal cases are taken into account. The corresponding nonsingular attitude maneuvering trajectories (i.e. open-loop control trajectories) with the consideration of a series of constraints are generated via Radau pseudospectral method. Compared with the traditional steering laws, the optimal steering law designed by this method can explicitly avoid the singularity from the global perspective. A linear quadratic regulator closed-loop controller is designed to guarantee the trajectory tracking performance in the presence of initial errors, inertia uncertainties and external disturbances. Simulation results verify the validity and feasibility of the proposed open-loop and closed-loop control methods.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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.

scholarly journals The Modelling, Simulation and FPGA-Based Implementation for Stepper Motor Wide Range Speed Closed-Loop Drive System Design

Machines ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 56 ◽  
Author(s):  
Chiu-Keng Lai ◽  
Jhang-Shan Ciou ◽  
Chia-Che Tsai
Keyword(s):  
Embedded System ◽  
High Speed ◽  
Closed Loop ◽  
Open Loop ◽  
Drive System ◽  
Stepper Motor ◽  
Motor Drive ◽  
Digital Controllers ◽  
Loop Control ◽  
Wide Range

Owing to the benefits of programmable and parallel processing of field programmable gate arrays (FPGAs), they have been widely used for the realization of digital controllers and motor drive systems. Furthermore, they can be used to integrate several functions as an embedded system. In this paper, based on Matrix Laboratory (Matlab)/Simulink and the FPGA chip, we design and implement a stepper motor drive. Generally, motion control systems driven by a stepper motor can be in open-loop or closed-loop form, and pulse generators are used to generate a series of pulse commands, according to the desired acceleration/run/deceleration, in order to the drive system to rotate the motor. In this paper, the speed and position are designed in closed-loop control, and a vector control strategy is applied to the obtained rotor angle to regulate the phase current of the stepper motor to achieve the performance of operating it in low, medium, and high speed situations. The results of simulations and practical experiments based on the FPGA implemented control system are given to show the performances for wide range speed control.

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.

scholarly journals Recovery of dynamics and function in spiking neural networks by closed-loop control

2015 ◽  
Author(s):  
Ioannis Vlachos ◽  
Taskin Deniz ◽  
Ad Aertsen ◽  
Arvind Kumar
Keyword(s):  
Neural Networks ◽  
Closed Loop ◽  
Brain Activity ◽  
Open Loop ◽  
Spiking Neural Networks ◽  
Delayed Feedback Control ◽  
Loop Control ◽  
Wide Range ◽  
Underlying Network ◽  
And Function

There is a growing interest in developing novel brain stimulation methods to control disease-related aberrant neural activity and to address basic neuroscience questions. Conventional methods for manipulating brain activity rely on open-loop approaches that usually lead to excessive stimulation and, crucially, do not restore the original computations performed by the network. Thus, they are often accompanied by undesired side-effects. Here, we introduce delayed feedback control (DFC), a conceptually simple but effective method, to control pathological oscillations in spiking neural networks. Using mathematical analysis and numerical simulations we show that DFC can restore a wide range of aberrant network dynamics either by suppressing or enhancing synchronous irregular activity. Importantly, DFC besides steering the system back to a healthy state, it also recovers the computations performed by the underlying network. Finally, using our theory we isolate the role of single neuron and synapse properties in determining the stability of the closed-loop system.

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 Behavioural system identification of visual flight speed control in Drosophila melanogaster

2010 ◽  
Vol 8 (55) ◽  
pp. 171-185 ◽  
Author(s):  
Nicola Rohrseitz ◽  
Steven N. Fry
Keyword(s):  
System Identification ◽  
Flight Control ◽  
Closed Loop ◽  
Speed Control ◽  
Control Model ◽  
Open Loop ◽  
Flight Speed ◽  
Level Control ◽  
Wide Range ◽  
Sensory Motor

Behavioural control in many animals involves complex mechanisms with intricate sensory-motor feedback loops. Modelling allows functional aspects to be captured without relying on a description of the underlying complex, and often unknown, mechanisms. A wide range of engineering techniques are available for modelling, but their ability to describe time-continuous processes is rarely exploited to describe sensory-motor control mechanisms in biological systems. We performed a system identification of visual flight speed control in the fruitfly Drosophila , based on an extensive dataset of open-loop responses previously measured under free flight conditions. We identified a second-order under-damped control model with just six free parameters that well describes both the transient and steady-state characteristics of the open-loop data. We then used the identified control model to predict flight speed responses after a visual perturbation under closed-loop conditions and validated the model with behavioural measurements performed in free-flying flies under the same closed-loop conditions. Our system identification of the fruitfly's flight speed response uncovers the high-level control strategy of a fundamental flight control reflex without depending on assumptions about the underlying physiological mechanisms. The results are relevant for future investigations of the underlying neuromotor processing mechanisms, as well as for the design of biomimetic robots, such as micro-air vehicles.

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