scholarly journals Commutativity of systems with their feedback conjugates

2018 ◽  
Vol 41 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Mehmet Emir Koksal
Keyword(s):  
Dynamical System ◽  
Differential System ◽  
Linear Time ◽  
Relevant Literature ◽  
Time Varying ◽  
Single Input Single Output ◽  
Single Output ◽  
Single Input

After introducing commutativity concept and summarizing the relevant literature, this work is focused on the commutativity of feedback conjugates. It is already known that a linear time-varying differential system describing a single input-single output dynamical system is always commutative with its constant gain feedback pairs. In this article, it is proven that among the time-varying feedback conjugates of a linear time-varying system, constant feedback conjugates are the only commutative feedback pairs and any of the time-varying feedback conjugates cannot constitute a commutative pair of a linear time-varying system.

Nonlinear PI Compensators That Achieve High Performance

1997 ◽  
Vol 119 (1) ◽  
pp. 105-110 ◽  
Author(s):  
S. M. Shahruz ◽  
A. L. Schwartz
Keyword(s):  
High Performance ◽  
Optimization Problem ◽  
Linear Time ◽  
Feedback System ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Single Input ◽  
Nonlinear Compensator ◽  
Time Invariant

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by a (linear) proportional and integral (PI) compensator are considered. For such systems a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution. Additionally, a general non-linear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over the linear PI compensator is discussed and is demonstrated for a feedback system.

Lumped and Distributed Parameter System Identification Via Shifted Legendre Polynomials

1988 ◽  
Vol 110 (4) ◽  
pp. 436-440 ◽  
Author(s):  
B. M. Mohan ◽  
K. B. Datta
Keyword(s):  
Linear Time ◽  
Operational Matrix ◽  
Distributed Parameter ◽  
Parameter System ◽  
Legendre Series ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Single Input ◽  
Time Invariant

In this paper, one shot operational matrix for repeated integration of the shifted Legendre polynomial basis vector is developed and double-shifted Legendre series is introduced to approximate functions of two independent variables. Then using these, systematic algorithms for the identification of linear time-invariant single input-single output continuous lumped and distributed parameter systems are presented. Illustrative examples are provided with satisfactory results.

Inverse control of single-input/single-output nonlinear time-varying systems with noise disturbances by multi-dimensional Taylor network

2020 ◽  
Vol 42 (13) ◽  
pp. 2450-2464
Author(s):  
Hong-Sen Yan ◽  
Chao Zhang
Keyword(s):  
Real Time ◽  
Recursive Least Squares ◽  
Time Varying ◽  
Single Input Single Output ◽  
Inverse Control ◽  
The Real ◽  
Single Output ◽  
Time Varying Systems ◽  
Single Input ◽  
Noise Disturbances

In this paper, an inverse control scheme based on the novel dynamic network (multi-dimensional Taylor network (MTN)) is proposed for the real-time tracking control of nonlinear time-varying systems with noise disturbances. Utilized in this scheme are the three MTNs: the adaptive model identifier for system modeling, the adaptive inverse controller for inverse modeling, and the adaptive nonlinear filter for eliminating the noise disturbances, whose weights are modified by the variable forgetting factor recursive least squares (VFF-RLS), back propagation through model (BPTM), normalized least mean square (NLMS) algorithms, respectively. To avoid “compromise”, this scheme is designed into a structure wherein controlling the object dynamic response and eliminating the noise disturbances are implemented in two relatively independent processes. Furthermore, the weight-elimination algorithm is introduced for choice of effective regression items to avoid the dimension explosion, thus overcoming the shortcoming that the number of middle nodes needs to be determined before using the traditional neural network. After a certain number of training, the more streamlined MTNs are observed to contribute to satisfying the real-time requirements of software implementation and engineering application. To ensure that MTN inverse control is strict in theory, the general conditions for the existence of single-input/single-output (SISO) nonlinear inverse systems are identified. Simulation of the MTN inverse control is conducted to confirm the effectiveness of the proposed method.

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