scholarly journals On the theory of constructive construction of a linear controller

2020 ◽  
Vol 16 (3) ◽  
pp. 326-344
Author(s):  
Alexander M. Kamachkin ◽  
◽  
Nikolai A. Stepenko ◽  
Gennady M. Chitrov ◽  
◽  
...  
Keyword(s):  
Classical Problem ◽  
Original System ◽  
Diagonal Form ◽  
Linear Controller ◽  
Controlled Systems ◽  
Linear Regulator ◽  
The Matrix ◽  
Zubov’S Method ◽  
Block Diagonal Form ◽  
Stationary Stabilization

The classical problem of stationary stabilization with respect to the state of a linear stationary control system is investigated. Efficient, easily algorithmic methods for constructing controllers of controlled systems are considered: the method of V. I. Zubov and the method of P. Brunovsky. The most successful modifications are indicated to facilitate the construction of a linear controller. A new modification of the construction of a linear regulator is proposed using the transformation of the matrix of the original system into a block-diagonal form. This modification contains all the advantages of both V. I. Zubov’s method and P. Brunovsky’s method, and allows one to reduce the problem with multidimensional control to the problem of stabilizing a set of independent subsystems with scalar control for each subsystem.

scholarly journals On the Parametric Solution to the Second-Order Sylvester Matrix EquationEVF2−AVF−CV=BW

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Wang Guo-Sheng ◽  
Lv Qiang ◽  
Duan Guang-Ren
Keyword(s):  
Control Systems ◽  
Matrix Equation ◽  
Second Order ◽  
Diagonal Form ◽  
Sylvester Matrix Equation ◽  
Parametric Solution ◽  
Design Problems ◽  
Analysis And Design ◽  
Sylvester Matrix ◽  
The Matrix

This paper considers the solution to a class of the second-order Sylvester matrix equationEVF2−AVF−CV=BW. Under the controllability of the matrix triple(E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrixFin a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.

Utilization of Control Effort Constraints in Linear Controller Design

1989 ◽  
Vol 111 (3) ◽  
pp. 378-381 ◽  
Author(s):  
A. Galip Ulsoy
Keyword(s):  
Feedback Control ◽  
Controller Design ◽  
Design Procedure ◽  
Maximum Energy ◽  
Control Effort ◽  
Single Input Single Output ◽  
State Variable ◽  
Linear Controller ◽  
Single Output ◽  
Controlled Systems

A linear controller design procedure, which accounts for constraints on control effort, is developed by requiring that the control system utilize the maximum energy delivering capability of the final control elements under some specified test conditions (e.g., maximum step reference input). Results using this approach are available from previous studies for low-order single-input single-output controlled systems. This paper presents results for multi-input multi-output systems where the number of inputs is equal to the number of states. Both state variable feedback control for regulation, and integral plus state variable feedback control for tracking are considered and illustrated with an example problem.

scholarly journals Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1590
Author(s):  
Georg Junker
Keyword(s):  
Quantum Dynamics ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Arbitrary Spin ◽  
Negative Energy ◽  
Diagonal Form ◽  
Proca Equation ◽  
Klein Gordon ◽  
Block Diagonal Form ◽  
Supersymmetric Structure

Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary but fixed spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. Here, the supercharges transform between energy eigenstates of positive and negative energy. For such supersymmetric Hamiltonians, an exact Foldy–Wouthuysen transformation exists which brings it into a block-diagonal form separating the positive and negative energy subspaces. The relativistic dynamics of a charged particle in a magnetic field are considered for the case of a scalar (spin-zero) boson obeying the Klein–Gordon equation, a Dirac (spin one-half) fermion and a vector (spin-one) boson characterised by the Proca equation. In the latter case, supersymmetry implies for the Landé g-factor g=2.

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