Control of a Class of Manipulators With a Single Flexible Link: Part II—Observer-Controller Stabilization

1991 ◽  
Vol 113 (4) ◽  
pp. 662-668 ◽  
Author(s):  
D. Wang ◽  
M. Vidyasagar
Keyword(s):  
State Space ◽  
State Feedback ◽  
Linear Part ◽  
The State ◽  
Observer Design ◽  
Input Output ◽  
Flexible Link ◽  
System Equations ◽  
Nonlinear State

In this paper, a controller and observer design is proposed for a class of multi-link manipulators with one flexible link. It is shown that it is possible to transform the state space equations of these manipulators into an equivalent set of equations which are almost linear. The controller then uses a nonlinear state feedback which is designed based only on the linear part of the transformed system equations. An observer is presented in which the estimated states converge to the actual states exponentially. Finally, it is shown that combining the observer with the controller results in a system which is input-output stable in a local sense.

scholarly journals Parameter and State Estimator for State Space Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ruifeng Ding ◽  
Linfan Zhuang
Keyword(s):  
State Space ◽  
State Equation ◽  
The State ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
State Variables ◽  
Input Output ◽  
State Estimator ◽  
Output Data ◽  
Canonical State

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.

scholarly journals State Feedback of Complex Systems Using Fuzzy Cognitive Maps

2018 ◽  
Vol 6 (3) ◽  
pp. 1-6 ◽  
Author(s):  
Vassiliki Mpelogianni ◽  
Ioannis Arvanitakis ◽  
Peter Groumpos
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
State Space ◽  
State Vector ◽  
State Feedback ◽  
Mathematical Formulation ◽  
Cognitive Maps ◽  
The State ◽  
Fuzzy Cognitive Maps ◽  
System Model

Complex systems have become a research area with increasing interest over the last years. The emergence of new technologies, the increase in computational power with reduced resources and cost, the integration of the physical world with computer based systems has created the possibility of significantly improving the quality of life of humans. While a significant degree of automation within these systems exists and has been provided in the past decade with examples of the smart homes and energy efficient buildings, a paradigm shift towards autonomy has been noted. The need for autonomy requires the extraction of a model; while a strict mathematical formulation usually exists for the individual subsystems, finding a complete mathematical formulation for the complex systems is a near impossible task to accomplish. For this reason, methods such as the Fuzzy Cognitive Maps (FCM) have emerged that are able to provide with a description of the complex system. The system description results from empirical observations made from experts in the related subject – integration of expert’s knowledge – that provide the required cause-effect relations between the interacting components that the FCM needs in order to be formulated. Learning methods are employed that are able to improve the formulated model based on measurements from the actual system. The FCM method, that is able to inherently integrate uncertainties, is able to provide an adequate model for the study of a complex system. With the required system model, the next step towards the development of a autonomous systems is the creation of a control scheme. While FCM can provide with a system model, the system representation proves inadequate to be utilized to design classic model based controllers that require a state space or frequency domain representation. In state space representation, the state vector contains the variables of the system that can describe enough about the system to determine its future behavior in absence of external variables. Thus, within the components – the nodes of the FCM, ideally those can be identified that constitute the state vector of the system. In this work the authors propose the creation of a state feedback control law of complex systems via Fuzzy Cognitive Maps. Given the FCM representation of a system, initially the components-states of the system are identified. Given the identified states, a FCM representation of the controller occurs where the controller parameters are the weights of the cause-effect relations of the system. The FCM of the system then is augmented with the FCM of the controller. An example of the proposed methodology is given via the use of the cart-pendulum system, a common benchmark system for testing the efficiency of control systems.

scholarly journals On the Stabilization and Observer Design of Polytopic Perturbed Linear Fractional-Order Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Omar Naifar ◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Fractional Order ◽  
State Feedback ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
Parameter Dependent ◽  
Lyapunov Technique

In this paper, the problem of stabilization and observer design of parameter-dependent perturbed fractional-order systems is investigated. Sufficient conditions on the practical Mittag–Leffler and Mittag–Leffler stability are given based on the Lyapunov technique. Firstly, the problem of stabilization using the state feedback is developed. Secondly, under some sufficient hypotheses, an observer design which provides an estimation of the state is constructed. Finally, numerical examples are provided to validate the contributed results.

scholarly journals The State Space Subdivision Filter for Estimation on SE(2)

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6314
Author(s):  
Florian Pfaff ◽  
Kailai Li ◽  
Uwe D. Hanebeck
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Unscented Kalman Filter ◽  
Linear Part ◽  
The State ◽  
Conditional Density ◽  
Periodic Part ◽  
Order Of Magnitude ◽  
Circular Domains ◽  
Position And Orientation

The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. We present a novel filter that involves splitting up the joint density into a (marginalized) density for the periodic part and a conditional density for the linear part. We subdivide the state space along the periodic dimension and describe each part of the state space using the parameters of a Gaussian and a grid value, which is the function value of the marginalized density for the periodic part at the center of the respective area. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the SE(2) domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. We thoroughly compared the filters with other state-of-the-art filters in a simulated tracking scenario. With only little run time, our filter outperformed an unscented Kalman filter for manifolds and a progressive filter based on dual quaternions. Our filter also yielded more accurate results than a particle filter using one million particles while being faster by over an order of magnitude.

Optimal control strategy of state feedback control for surface-mounted PMSM drives based on auto-tuning of seeker optimization algorithm

2021 ◽  
pp. 1-21
Author(s):  
Junhao Cao ◽  
Xiaodong Sun ◽  
Xiang Tian
Keyword(s):  
Optimal Control ◽  
State Space ◽  
Optimization Algorithm ◽  
State Feedback ◽  
State Space Model ◽  
The State ◽  
Load Torque ◽  
Space Model ◽  
Auto Tuning ◽  
Seeker Optimization Algorithm

This paper focus on a state feedback controller (SFC)-based optimal control scheme for surface-mounted permanent-magnet synchronous motor (SPMSM) with auto-tuning of controller built on seeker optimization algorithm (SOA). First, based on the nonlinear state-space model of SPMSM, voltage feedforward compensation is used to design a linear SFC. Then in order to guarantee the steady performance in speed and current, integral models considering the errors of rotor speed and current response in d-axis are added in the state space model of SPMSM. Furthermore, by statically decoupling the load torque in the state equation, feedforward compensation is implemented on the load torque to improve the dynamic performance of the controller. The load torque is estimated using disturbance observer with reasonable parameter selection. Then, with the consideration of the search capacity of seeker optimization algorithm (SOA), it is adopted to acquire matrix coefficient of the presented controller. Furthermore, in order to suppress the speed overshoot, a penalty term is introduced to the fitness index. The performance of the proposed method has been validated experimentally and compared with the conventional method under different conditions.

Application of local coordinates rectification in linearization of selected parameters of dynamic nonlinear systems

2014 ◽  
Vol 33 (5) ◽  
pp. 1819-1830 ◽  
Author(s):  
Andrzej Zawadzki
Keyword(s):  
Nonlinear System ◽  
Coordinate System ◽  
State Space ◽  
State Equation ◽  
The State ◽  
Content Type ◽  
Electric Circuits ◽  
First Order ◽  
State Space Transformation ◽  
Nonlinear State

Purpose – The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form. Design/methodology/approach – It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system. Findings – The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input – the state of the nonlinear system). Originality/value – Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.

Plant-Input-Mapping Discretization Method for a Feedback System in the State-Space Form

2021 ◽  
Author(s):  
Keisuke Yagi ◽  
Hiroaki Muto ◽  
Yoshikazu Mori
Keyword(s):  
Transfer Function ◽  
State Space ◽  
State Feedback ◽  
Closed Loop ◽  
Space Form ◽  
Feedback System ◽  
The State ◽  
Loop System ◽  
Closed Loop System ◽  
Digital Redesign

Abstract The paper proposes the digital redesign technique called plant-input-mapping (PIM) method for a feedback system described in the state-space form. The PIM method, which was originally presented in the transfer function form, focuses on the plant input signal via the plant input transfer function and discretizes it so as to satisfy the control zero principle in the resulting discrete-time closed-loop system, which leads to guaranteeing the closed-loop stability for any non-pathological sampling interval. In accordance with this approach, the proposed PIM method focuses on the control zeros included in the plant input signal. The paper proves that the matched-pole-zero discrete-time model of the plant input state-equation satisfies the control zero principle with the step-invariant model of the plant. Then, when the matched-pole-zero model is set as the target of model matching, the parameters of the state-space PIM controller employing the observer-based dynamic state-feedback can systematically be determined from the underlying continuous-time closed-loop system with guaranteed stability. This discretization process can immediately be applied to a state-feedback system and a class of multi-input multi-output systems without any modification, which cannot be discretized by the conventional PIM methods. The discretization performance of the proposed PIM method is evaluated through illustrative examples with comparable digital redesign methods, which reveal that the proposed method performs a good reproduction of the characteristics of the underlying closed-loop system.

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