Generalized Arnoldi methods for the Sylvester-observer equation and the multi-input pole placement problem

An analytical model predictive control (MPC) tuning method for multivariable first-order plus fractional dead time systems is presented in this paper. First, the decoupling condition of the closed-loop system is derived, based on which the considered multivariable MPC tuning problem is simplified to a pole placement problem. Given such a simplification, an analytical tuning method guaranteeing the closed-loop stability as well as pre-specified time-domain performance is developed. Finally, simulation examples are provided to show the effectiveness of the proposed method.

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A Study into the Relationship between the Procedures for the Pole Placement Problem and Linear Quadratic Regulator

2018 IEEE XXVII International Scientific Conference Electronics - ET ◽

10.1109/et.2018.8549659 ◽

2018 ◽

Author(s):

Nasko Raychev Atanasov ◽

Mariela Ivanova Alexandrova ◽

Ivan Veselinov Grigorov ◽

Ivelina Yordanova Zlateva

Keyword(s):

Linear Quadratic Regulator ◽

Pole Placement ◽

Linear Quadratic ◽

Placement Problem ◽

The Relationship

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Optimum Design of Control System Compensators By Geometric Programming

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3149588 ◽

1980 ◽

Vol 102 (2) ◽

pp. 106-113 ◽

Cited By ~ 3

Author(s):

E. V. Bohn

Keyword(s):

Control System ◽

Time Delay ◽

Optimum Design ◽

Geometric Programming ◽

Necessary Conditions ◽

Pole Placement ◽

Programming Approach ◽

Placement Problem ◽

Delay Response ◽

Compensator Design

A process of condensation is used to develop a geometric programming approach to the necessary conditions for a constrained optimum in an elementary way. Special features of geometric programming not found in other optimization procedures and which offer significant advantages in the design of optimum compensators are developed. Compensator design is formulated as an optimum pole placement problem subject to a time delay response constraint. The geometric programming approach results in simple explicit equations for the optimum compensator parameters.

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Generic Properties of the Pole Placement Problem

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)66142-1 ◽

1978 ◽

Vol 11 (1) ◽

pp. 1725-1729 ◽

Cited By ~ 33

Author(s):

J.C. Willems ◽

W.H. Hesselink

Keyword(s):

Pole Placement ◽

Generic Properties ◽

Placement Problem

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Pole Placement for Single-Input Linear System by Proportional-Derivative State Feedback

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4028713 ◽

2014 ◽

Vol 137 (4) ◽

Cited By ~ 4

Author(s):

Taha H. S. Abdelaziz

Keyword(s):

Linear System ◽

Linear Systems ◽

Degrees Of Freedom ◽

State Feedback ◽

Pole Placement ◽

Feedback Gain ◽

Time Varying ◽

Placement Problem ◽

Single Input ◽

Time Invariant

This paper deals with the direct solution of the pole placement problem for single-input linear systems using proportional-derivative (PD) state feedback. This problem is always solvable for any controllable system. The explicit parametric expressions for the feedback gain controllers are derived which describe the available degrees of freedom offered by PD state feedback. These freedoms are utilized to obtain closed-loop systems with small gains. Its derivation is based on the transformation of linear system into control canonical form by a special coordinate transformation. The solving procedure results into a formula similar to Ackermann’s one. In the present work, both time-invariant and time-varying linear systems are treated. The effectiveness of the proposed method is demonstrated by the simulation examples of both time-invariant and time-varying systems.

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