scholarly journals A Direct Algorithm for Pole Placement by State-derivative Feedback for Single-input Linear Systems

10.14311/500 ◽  
2003 ◽  
Vol 43 (6) ◽  
Author(s):  
Taha H. S. Abdelaziz ◽  
M. Valášek
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Closed Loop ◽  
Original System ◽  
Pole Placement ◽  
Time Varying ◽  
Placement Problem ◽  
Input System ◽  
Single Input ◽  
Controllable Systems

This paper deals with the direct solution of the pole placement problem for single-input linear systems using state-derivative feedback. This pole placement problem is always solvable for any controllable systems if all eigenvalues of the original system are nonzero. Then any arbitrary closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results in a formula similar to the Ackermann formula. Its derivation is based on the transformation of a linear single-input system into Frobenius canonical form by a special coordinate transformation, then solving the pole placement problem by state derivative feedback. Finally the solution is extended also for single-input time-varying control systems. The simulation results are included to show the effectiveness of the proposed approach.

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

2014 ◽  
Vol 137 (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.

scholarly journals Partial Pole Placement in LMI Region

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Liuli Ou ◽  
Shaobo Han ◽  
Yongji Wang ◽  
Shuai Dong ◽  
Lei Liu
Keyword(s):  
Closed Loop ◽  
Pole Placement ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Region ◽  
Placement Problem ◽  
New Approach ◽  
Input System ◽  
Single Input ◽  
Lmi Region

A new approach for pole placement of single-input system is proposed in this paper. Noncritical closed loop poles can be placed arbitrarily in a specified convex region when dominant poles are fixed in anticipant locations. The convex region is expressed in the form of linear matrix inequality (LMI), with which the partial pole placement problem can be solved via convex optimization tools. The validity and applicability of this approach are illustrated by two examples.

A New Direct Algorithm for Pole-Placement by State-Derivative Feedback for Single-Input Linear Systems

2013 ◽  
Vol 423-426 ◽  
pp. 2869-2872
Author(s):  
Zun Hai Gao
Keyword(s):  
Linear Systems ◽  
Characteristic Polynomial ◽  
Canonical Form ◽  
General Expression ◽  
Pole Placement ◽  
Feedback Gain ◽  
Direct Algorithm ◽  
Gain Matrix ◽  
Input System ◽  
Single Input

The generalized Wonham controllable canonical form in single-input systems is presented and applied to pole placement of state derivative feedback. A new direct algorithm is proposed. The advantage of this algorithm is no need to compute the characteristic polynomial of the system. The theory and approach are introduced, and the general expression is obtained for the derivative feedback gain matrix of the single-input system.

A New Direct Algorithm for Pole Placement by State-Derivative Feedback for Multi-Input Linear Systems

2013 ◽  
Vol 433-435 ◽  
pp. 1021-1024
Author(s):  
Zun Hai Gao
Keyword(s):  
Linear Systems ◽  
Characteristic Polynomial ◽  
Canonical Form ◽  
General Expression ◽  
Pole Placement ◽  
Feedback Gain ◽  
Arbitrary Parameter ◽  
Direct Algorithm ◽  
Input System ◽  
Single Input

The generalized Wonham controllable canonical form in multi-input systems is presented and applied to pole placement of state derivative feedback. A new direct algorithm is proposed. The multi-input system can be decomposed some single-input systems and for every single-input system the problem is easy to be resolved. The advantage of this algorithm is no need to compute the characteristic polynomial of the system. The theory and approach are introduced, and the general expression containing arbitrary parameter is obtained for the derivative feedback gain matrix of the multi-input system. An illustrative example is presented to show the proposed method.

scholarly journals On the selection of poles in the single-input pole placement problem

1999 ◽  
Vol 302-303 ◽  
pp. 331-345 ◽  
Author(s):  
D. Calvetti ◽  
B. Lewis ◽  
L. Reichel
Keyword(s):  
Pole Placement ◽  
Placement Problem ◽  
Input Pole ◽  
Single Input ◽  
Selection Of

scholarly journals Analytical Tuning Method of MPC Controllers for MIMO First-Order Plus Fractional Dead Time Systems

Processes ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 212
Author(s):  
Ning He ◽  
Yichun Jiang ◽  
Lile He
Keyword(s):  
Predictive Control ◽  
Closed Loop ◽  
Dead Time ◽  
Pole Placement ◽  
Closed Loop System ◽  
Placement Problem ◽  
First Order ◽  
Tuning Method ◽  
Domain Performance ◽  
Time Systems

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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