An L1 adaptive closed-loop guidance law for an orbital injection problem

2009 ◽  
Vol 223 (6) ◽  
pp. 753-761 ◽  
Author(s):  
J Roshanian ◽  
M Zareh ◽  
H H Afshari ◽  
M Rezaei
Keyword(s):  
Closed Loop ◽  
Adaptive Strategy ◽  
Analytical Form ◽  
Open Loop ◽  
Control Input ◽  
Guidance Law ◽  
Non Linear ◽  
Non Linear System ◽  
Orbital Injection

The current paper presents the determination of a closed-loop guidance law for an orbital injection problem using two different approaches and, considering the existing time-optimal open-loop trajectory as the nominal solution, compares the advantages of the two proposed strategies. In the first method, named neighbouring optimal control (NOC), the perturbation feedback method is utilized to determine the closed-loop trajectory in an analytical form for the non-linear system. This law, which produces feedback gains, is in general a function of small perturbations appearing in the states and constraints separately. The second method uses an L1 adaptive strategy in determination of the non-linear closed-loop guidance law. The main advantages of this method include characteristics such as improvement of asymptotic tracking, guaranteed time-delay margin, and smooth control input. The accuracy of the two methods is compared by introducing a high-frequency sinusoidal noise. The simulation results indicate that the L1 adaptive strategy has a better performance than the NOC method to track the nominal trajectory when the noise amplitude is increased. On the other hand, the main advantage of the NOC method is its ability to solve a non-linear, two-point, boundary-value problem in the minimum time.

Design of H_/H∞ fault detection observer for closed-loop nonlinear system with disturbance

2020 ◽  
Vol 40 (4) ◽  
pp. 589-599
Author(s):  
Zhengquan Chen ◽  
Lu Han ◽  
Yandong Hou
Keyword(s):  
Fault Detection ◽  
Closed Loop ◽  
External Disturbance ◽  
Adaptive Threshold ◽  
Linear Matrix ◽  
Content Type ◽  
Non Linear ◽  
Runge Kutta ◽  
Non Linear System ◽  
Residual Generator

Purpose This paper proposes a novel method of fault detection, which is based on H_/H∞ Runge–Kutta observer and an adaptive threshold for a class of closed-loop non-linear systems. The purpose of this paper is to improve the rapidity and accuracy of fault detection. Design/methodology/approach First, the authors design the H_/H∞ Runge–Kutta fault detection observer, which is used as a residual generator to decouple the residual from the input. The H_ performance index metric in the specified frequency domain is used to describe how sensitive the residual to the fault. The H∞ norm is used to describe the residual robustness to the external disturbance of the systems. The residual generator is designed to achieve the best tradeoff between robustness against unknown disturbances but sensitivity to faults, thus realizing the accurate detection of the fault by suppressing the influence of noise and disturbance on the residual. Next, the design of the H_/H∞ fault detection observer is transformed into a convex optimization problem and solved by linear matrix inequality. Then, a new adaptive threshold is designed to improve the accuracy of fault detection. Findings The effectiveness and correctness of the method are tested in simulation experiments. Originality/value This paper presents a novel approach to improve the accuracy and rapidity of fault detection for closed-loop non-linear system with disturbances and noise.

Observer-based digital tracker for the manoeuvring target described by the continuous-time non-linear dynamic system

2008 ◽  
Vol 222 (2) ◽  
pp. 213-228 ◽  
Author(s):  
J S H Tsai ◽  
C T Wang ◽  
S M Guo ◽  
L S Shieh ◽  
C R Liu
Keyword(s):  
Dynamic System ◽  
Continuous Time ◽  
High Gain ◽  
Linear Dynamic System ◽  
Practical Implementation ◽  
Control Effort ◽  
Linear Dynamic ◽  
Guidance Law ◽  
Non Linear ◽  
Non Linear System

The current paper develops an effective and robust digital guidance law to intercept the highly manoeuvring target described by the continuous-time non-linear dynamic system. First, an optimal linearization model for the non-linear system is constructed at the operating point of interest on the trajectory. Then, high-gain optimal linear quadratic analogue tracker and observer are designed by utilizing the optimal linearization model and the optimal control theory, so that the effect of the unpredictable acceleration of the target can be substantially attenuated and even can be disregarded. For reducing the control effort without raising the prescribed interception time, and for practical implementation of the designed tracker, the prediction-based digital redesign method is utilized to obtain relatively low-gain digital tracker and observer from the well-designed high-gain optimal analogue tracker and observer. With the aid of the global positioning system, the proposed observer-based digital tracker is able to successfully intercept a highly manoeuvring target without the constraint on initial trajectory, and can effectively deal with various barriers during the interception. Illustrative examples are given to demonstrate the effectiveness and robustness of the proposed digital guidance law.

scholarly journals Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

2018 ◽  
Vol 28 (3) ◽  
pp. 457-472 ◽  
Author(s):  
José V. Salcedo ◽  
Miguél Martínez ◽  
Sergio García-Nieto ◽  
Adolfo Hilario
Keyword(s):  
Continuous Time ◽  
Closed Loop ◽  
Input Saturation ◽  
Fuzzy Model ◽  
Maximum Volume ◽  
Ts Fuzzy Model ◽  
Non Linear ◽  
Non Linear System ◽  
Takagi Sugeno ◽  
Fuzzy State

Abstract This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi-Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

Dynamic Emulation Using an Indirect Control Input

2004 ◽  
Vol 127 (1) ◽  
pp. 114-124 ◽  
Author(s):  
Rong Zhang ◽  
Andrew G. Alleyne
Keyword(s):  
Closed Loop ◽  
Open Loop ◽  
Control Input ◽  
Available Bandwidth ◽  
High Frequency Response ◽  
Physical Plant ◽  
Generalized Framework ◽  
Dynamic Emulation ◽  
Primary Focus ◽  
Output Only

This paper presents a generalized framework to analyze and design controllers for a class of dynamic emulation systems. This class of systems features some structurally distinctive control frameworks which inherently limit the available bandwidth for dynamic emulation. The primary focus is on control structures that we define as indirect. This means the signal from the controller does not affect the physical plant directly; it interacts in combination with other exogenous signals to affect a behavior on the physical system interacting with the emulated load. It is shown that the achievable closed-loop performance is limited in a unique way: the high-frequency response of the controlled closed-loop system converges to the dynamics of the open-loop physical plant that is interacting with the emulated load. This paper illustrates the three controller configurations of the indirect emulation and gives guidelines on how to improve the performance within the identified structural limitations. The three configurations are: a feedback design measuring plant output only, a feedforward design measuring an exogenous signal, and a two degree-of-freedom design combining feedback and feedforward measurements. A detailed analysis in the frequency domain is used to support the experimental results illustrated on a Hardware-in-the-Loop (HIL) system. The demonstration case is a high-bandwidth transient dynamometer to emulate rapidly varying loads associated with an earthmoving vehicle powertrain.

scholarly journals Implicit Euler Implementation of Twisting Controller and Super-Twisting Observer without Numerical Chattering: Precise Quasi-Static MEMS Mirrors Control

2019 ◽  
Vol 256 ◽  
pp. 03004 ◽  
Author(s):  
Dong Luo ◽  
Xiaogang Xiong ◽  
Shanhai Jin ◽  
Wei Chen
Keyword(s):  
Sliding Mode Control ◽  
Closed Loop ◽  
Sliding Mode ◽  
Industrial Applications ◽  
Euler Method ◽  
Open Loop ◽  
Closed Loop Control ◽  
Control Input ◽  
Loop Control ◽  
Mode Control

The quasi-static operations of MEMS mirror are very sensitive to undesired oscillations due to its very low damping. It has been shown that closed-loop control can be superior to reduce those oscillations than open-loop control in the literature. For the closed-loop control, the conventional way of implementing sliding mode control (SMC) algorithm is forward Euler method, which results in numerical chattering in the control input and output. This paper proposes an implicit Euler implementation scheme of super twisting observer and twisting control for a commercial MEMS mirror actuated by an electrostatic staggered vertical comb (SVC) drive structure. The famous super-twisting algorithm is used as an observer and twisting SMC is used as a controller. Both are discretized by an implicit Euler integration method, and their implementation algorithms are provided. Simulations verify that, as compared to traditional sliding mode control implementation, the proposed scheme reduces the chattering both in trajectory tracking output and control input in presence of model uncertainties and external disturbances. The comparison demonstrates the potential applications of the proposed scheme in industrial applications in terms of feasibility and performance.

Gain Settings for Specified Time Responses

1978 ◽  
Vol 11 (12) ◽  
pp. 461-468 ◽  
Author(s):  
E. C. Hind
Keyword(s):  
Phase Angle ◽  
Closed Loop ◽  
Open Loop ◽  
Loop Gain ◽  
Velocity Constant ◽  
Frequency Responses

A method is shown for the determination of gain settings for specified time responses from the open loop frequency responses. It is based on the use of the contour of constant closed loop phase angle, α = −90°. The method primarily yields the value of the static loop gain or velocity constant which is required so that the closed loop response will have a specified value of relative damping. For most systems, the solution is simple and direct.

Sign in / Sign up

Export Citation Format

Share Document