scholarly journals Circuits with a mem-element: invariant manifolds control via pulse programmed sources

2021 ◽  
Author(s):  
Mauro Di Marco ◽  
Giacomo Innocenti ◽  
Alberto Tesi ◽  
Mauro Forti
Keyword(s):  
Invariant Manifolds ◽  
Linear Time ◽  
Operational Amplifiers ◽  
Time Interval ◽  
State Variables ◽  
Finite Time Interval ◽  
Independent Source ◽  
Linear Time Invariant ◽  
Terminal Element ◽  
Time Invariant

AbstractThe paper considers the problem of controlling multistability in a general class of circuits composed of a linear time-invariant two-terminal (one port) element, containing linear R, L, C components and ideal operational amplifiers, coupled with one of the mem-elements (memory elements) introduced by Prof. L.O. Chua, i.e., memristors, memcapacitors, and meminductors. First, explicit expressions of the invariant manifolds of the circuit are directly given in terms of the state variables of the two-terminal element and the mem-element. Then, the problem of steering the circuit dynamics from an initial invariant manifold to a final one, and hence to potentially switch among different attractors of the circuit, is addressed by designing pulse shaped control inputs. The control inputs ensure that the transition between the initial and final manifolds is accomplished within a given finite time interval. Moreover, it is shown how the designed control inputs can be implemented by introducing independent voltage and current sources in the two-terminal element. Notably, it turns out that it is always possible to solve the considered control problem by using a unique independent source. Several examples are provided to illustrate how the proposed approach can be applied to different circuits with mem-elements and to highlight the influence of the features of the designed sources on the behavior of the controlled dynamics.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Linear Approximations for Swing Leg Motion During Gait

1984 ◽  
Vol 106 (2) ◽  
pp. 137-143 ◽  
Author(s):  
W. H. Lee ◽  
J. M. Mansour
Keyword(s):  
Linear Systems ◽  
System Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
State Variables ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Leg Motion ◽  
Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

A Time Delay Controller for Systems With Unknown Dynamics

1990 ◽  
Vol 112 (1) ◽  
pp. 133-142 ◽  
Author(s):  
Kamal Youcef-Toumi ◽  
Osamu Ito
Keyword(s):  
Time Delay ◽  
Control Method ◽  
Linear Time ◽  
Structure Stability ◽  
State Variables ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Single Input ◽  
Time Invariant

This paper focuses on the control of systems with unknown dynamics and deals with the class of systems described by x˙=f(x,t) + h(x,t) + B(x,t)u + d(t) where h(x,t) and d(t) are unknown dynamics and unexpected disturbances, respectively. A new control method, Time Delay Control (TDC), is proposed for such systems. Under the assumption of accessibility to all the state variables and estimates of their delayed derivatives, the TDC is characterized by a simple estimation technique that evaluates a function representing the effect of uncertainties. This is accomplished using time delay. The control system’s structure, stability and design issues are discussed for linear time-invariant and single-input-single-output systems. Finally, the control performance was evaluated through both simulations and experiments. The theoretical and experimental results indicate that this control method shows excellent robustness properties to unknown dynamics and disturbances.

scholarly journals PI observer stability and application in an induction motor control system

2013 ◽  
Vol 61 (3) ◽  
pp. 595-598 ◽  
Author(s):  
T. Białoń ◽  
A. Lewicki ◽  
M. Pasko ◽  
R. Niestrój
Keyword(s):  
Control System ◽  
Induction Motor ◽  
Linear Time ◽  
State Variables ◽  
Proportional Integral ◽  
Linear Time Invariant ◽  
Luenberger Observer ◽  
Motor Control System ◽  
Time Invariant ◽  
Proper Operation

Abstract The paper discusses the problem of stability of a proportional-integral Luenberger observer, designated for the state variables reconstruction of a linear, time-invariant dynamical system. It is proven, that there exists such a class of observed systems, for which the observer is always unstable, independently of its gains. Stability can be provided in every possible case after application of proposed modifications to the structure of the observer. It is proven, that stability of the modified observer depends only on its gains. It is shown, that an induction motor is the exemplary observed system, for which application of the unmodified observer is impossible due to its lack of stability, while the modified observer provides proper operation of the control system. Finally, some experimental results are presented, obtained in the multiscalar control system of the induction motor, equipped with the modified proportional-integral observer.

Application of a Robust Minimum-Order Observer to Control the Performance of an Uncertain Multivariable Boiler Unit

2010 ◽  
Author(s):  
Hamed Moradi ◽  
Firooz Bakhtiari-Nejad
Keyword(s):  
Linear Time ◽  
Mechanical Energy ◽  
Internal Variables ◽  
Feed Water ◽  
Boiler Unit ◽  
State Variables ◽  
Minimum Order ◽  
Linear Time Invariant ◽  
System A ◽  
Time Invariant

To obtain economic operation of power plant steam generators, output of mechanical energy must be balanced with the electrical load while maintaining the internal variables within desired ranges. During a boiler unit operation, dynamic variables such as drum pressure, steam temperature and water level of drum must be controlled to achieve an appropriate performance. In this paper, a linear time invariant (LTI) model of a boiler unit is considered where feed-water and fuel mass rates are the control inputs. Due to the inaccessibility of some state variables of boiler system, a robust minimum-order observer is designed to gain an estimate state of the true state. Real dynamic model of boiler unit may associate with parametric uncertainties. In this case, optimum region of poles of observer-based controller are found such that the robust performance of the boiler system against model uncertainties is guaranteed.

Steady state determination using bond graphs for systems with singular state matrix

2011 ◽  
Vol 225 (7) ◽  
pp. 887-901 ◽  
Author(s):  
G González A ◽  
R Galindo
Keyword(s):  
Steady State ◽  
State Space ◽  
Linear Time ◽  
Bond Graph ◽  
State Variables ◽  
Bond Graphs ◽  
State Matrix ◽  
Independent State ◽  
Linear Time Invariant ◽  
Time Invariant

A bond graph procedure to get the steady state value for linear time-invariant systems is presented. The general case of a singular state matrix is considered. The procedure is based on a junction structure configuration with derivative causality assignment, and on relationships of the bond graphs with integral and derivative causality assignments. It is shown that the structurally null modes, i.e. the poles at the origin, are cancelled for steady state. The key to cancel the poles at the origin is that the adjugate matrix of sIn −  Ap multiplies Bp yielding the zeros at the origin with the same order that the structurally null modes, where ( Ap, Bp, Cp, Dp) is a state space realization of a linear time-invariant system, s is the Laplace operator and In, is an n ×  n identity matrix. Hence, this unstable part of the system is cancelled and the steady state can be obtained. Thus, the singularity of the state space matrix is avoided, and the steady state is obtained from the bond graph with derivative causality assignment. Since the singular state matrix is considered, it is shown that by using the bond graph with derivative causality assignment, an equivalent system with linearly independent state variables can be obtained. An example of an electrical system with an electrical transformer modelled by an I-field whose state matrix is singular is presented. Also, the proposed methodology for a load driven by two DC motors is applied.

Sign in / Sign up

Export Citation Format

Share Document