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.

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.

Proportional–integral–derivative controller family for pole placement

2016 ◽  
Vol 231 (20) ◽  
pp. 3791-3797 ◽  
Author(s):  
Chimpalthradi R Ashokkumar ◽  
George WP York ◽  
Scott F Gruber
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Proportional Integral Derivative ◽  
Proportional Integral Derivative Controller ◽  
Proportional Integral ◽  
Linear Time Invariant ◽  
Generalized Eigenvalue ◽  
Square Systems ◽  
Time Invariant

In this paper, linear time-invariant square systems are considered. A procedure to design infinitely many proportional–integral–derivative controllers, all of them assigning closed-loop poles (or closed-loop eigenvalues), at desired locations fixed in the open left half plane of the complex plane is presented. The formulation accommodates partial pole placement features. The state-space realization of the linear system incorporated with a proportional–integral–derivative controller boils down to the generalized eigenvalue problem. The generalized eigenvalue-eigenvector constraint is transformed into a system of underdetermined linear homogenous set of equations whose unknowns include proportional–integral–derivative parameters. Hence, the proportional–integral–derivative solution sets are infinitely many for the chosen closed-loop eigenvalues in the eigenvalue-eigenvector constraint. The solution set is also useful to reduce the tracking errors and improve the performance. Three examples are illustrated.

A Geometric Representation of Root Sensitivity

1994 ◽  
Vol 116 (2) ◽  
pp. 305-309 ◽  
Author(s):  
T. R. Kurfess ◽  
M. L. Nagurka
Keyword(s):  
Control System ◽  
System Design ◽  
Dynamic Systems ◽  
Linear Time ◽  
Sensitivity Function ◽  
Control System Design ◽  
Geometric Representation ◽  
Root Locus ◽  
Linear Time Invariant ◽  
Time Invariant

In this paper, we present a geometric method for representing the classical root sensitivity function of linear time-invariant dynamic systems. The method employs specialized eigenvalue plots that expand the information presented in the root locus plot in a manner that permits determination by inspection of both the real and imaginary components of the root sensitivity function. We observe relationships between root sensitivity and eigenvalue geometry that do not appear to be reported in the literature and hold important implications for control system design and analysis.

An Equivalent Plant Representation for Unknown Control Systems

2014 ◽  
Author(s):  
Daniel N. Mohsenizadeh ◽  
Lee H. Keel ◽  
Shankar P. Bhattacharyya
Keyword(s):  
Complex System ◽  
Control System ◽  
Control Systems ◽  
Linear Time ◽  
Stability Margins ◽  
Linear Time Invariant ◽  
Plant Construction ◽  
Small Set ◽  
Unknown Control ◽  
Time Invariant

This paper proposes a new method to the design of a controller to be embedded at a prescribed location in an otherwise unknown complex and multiple-loop Linear Time-Invariant (LTI) control system. The questions that arise naturally are: Will a controller proposed for this location stabilizes the overall system and, if so, what stability margins and response can be obtained? We address these questions by constructing an equivalent single-loop frequency domain representation of the original unknown complex system. This equivalent plant construction can be accomplished by a small set of frequency response measurements.

Analysis of an Error Integral Driven MIMO SM Regulator for LTI Systems

2016 ◽  
Author(s):  
Kerim Yunt
Keyword(s):  
Parameter Uncertainty ◽  
Sliding Mode ◽  
Linear Time ◽  
Pole Placement ◽  
Sliding Mode Controller ◽  
Minimum Phase ◽  
Linear Time Invariant ◽  
Luenberger Observer ◽  
Optimization Routine ◽  
Time Invariant

In this work an error-integral-driven sliding mode controller (EID-SMC) for multi-input multi-output (MIMO) minimum phase linear time-invariant (LTI) systems with feedthrough controls and output disturbance is analyzed. Though the sliding variable remains in the vicinity of the sliding surface without reaching it, it is shown that the steady-state error vanishes exponentially asymptotically within the boundary layer even if parameter uncertainty and unmatched input/output disturbances exist. The pole-placement is accomplished indirectly by an iterative optimization routine by considering limits on controls and state contrary to the existing practice in SMC where either direct pole placement or quadratic norm optimality of a performance is used. For the proposed controller framework the Luenberger observer is presented.

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 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.

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