Parametric eigenvalue assignment by constant output feedback – a cascaded approach

2020 ◽  
Vol 68 (10) ◽  
pp. 817-825
Author(s):  
Ulrich Konigorski
Keyword(s):  
Output Feedback ◽  
Degrees Of Freedom ◽  
Design Procedure ◽  
Feedback Gain ◽  
Spectral Condition ◽  
Closed Loop System ◽  
Control Scheme ◽  
Constant Output ◽  
System States ◽  
Eigenvalue Assignment

AbstractIn this paper a numerical efficient approach to the problem of eigenvalue assignment by constant output feedback is presented. It improves the well known Kimura’s condition by 2, i. e., it is shown that if m+p\ge n-1 generically a solution to this design problem exists where n,m and p denote the dimensions of the system states, inputs and outputs, respectively. The algorithm is based on a cascaded control scheme with up to three design steps. The first two steps merely require standard methods from linear algebra while the last step only in case of m+p=n-1 demands for the numerical solution of a system of three polynomial equations each of order two. The design procedure explicitly embodies all degrees of freedom beyond eigenvalue assignment. Thus, they can be used to account for other design it is shown goals, e. g., to minimize the spectral condition number of the closed-loop system or a norm of the feedback gain as it is shown by numerical examples from literature.

A Note on Pole Placement of Mechanical Systems

1991 ◽  
Vol 113 (3) ◽  
pp. 420-421 ◽  
Author(s):  
C. Minas ◽  
D. J. Inman
Keyword(s):  
Least Squares ◽  
Canonical Form ◽  
Output Feedback ◽  
Closed Loop ◽  
Weighted Least Squares ◽  
Mechanical Systems ◽  
Pole Placement ◽  
Feedback Gain ◽  
Closed Loop System ◽  
Feedback Method

An output feedback method is developed, that systematically places a desired number of poles of a closed-loop system at or near desired locations. The system is transformed to its equivalent controllable canonical form, where the output feedback gain matrix is calculated in a weighted least squares scheme, that minimizes the change of the remaining modes of the system. The advantage of this method over other pole placement routines is the fact that the influence on the remaining unplaced modes of the system is minimum, which is particularly important in preserving closed-loop stability.

scholarly journals Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Mounir Hammouche ◽  
Philippe Lutz ◽  
Micky Rakotondrabe
Keyword(s):  
State Space ◽  
Output Feedback ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
State Space Model ◽  
Output Feedback Control ◽  
Optimal Solution ◽  
Loop System ◽  
Closed Loop System ◽  
Optimal Output

The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.

Stabilization of Fractional-Order Systems Subject to Saturation Element Using Fractional Dynamic Output Feedback Sliding Mode Control

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Esmat Sadat Alaviyan Shahri ◽  
Alireza Alfi ◽  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Linear Component ◽  
Dynamic Output Feedback ◽  
Closed Loop System ◽  
Fractional Systems ◽  
Dynamic Output ◽  
System States

This paper addresses the design of a robust fractional-order dynamic output feedback sliding mode controller (FDOF-SMC) for a general class of uncertain fractional systems subject to saturation element. The control law is composed of two components, one linear and one nonlinear. The linear component corresponds to the fractional-order dynamics of the FDOF-SMC, while the nonlinear component is associated with the switching control algorithm. The closed-loop system exhibits asymptotical stability and the system states approach the sliding surface in a finite time. In order to design the controller, a linear matrix inequality (LMI)-based procedure is also derived. Simulation results demonstrate the feasibility of the FDOF-SMC strategy.

An Approach to Partial Quadratic Eigenvalue Assignment of Damped Vibration Systems Using Static Output Feedback

2018 ◽  
Vol 18 (01) ◽  
pp. 1850012 ◽  
Author(s):  
Jiafan Zhang ◽  
Yongxin Yuan ◽  
Hao Liu
Keyword(s):  
Output Feedback ◽  
Second Order ◽  
Order System ◽  
Feedback Gain ◽  
Static Output Feedback ◽  
Homogeneous Matrix ◽  
Quadratic Eigenvalue ◽  
Static Output ◽  
Damped Vibration Systems ◽  
Eigenvalue Assignment

This paper addresses the problem of the partial eigenvalue assignment for second-order damped vibration systems by static output feedback. The presented method uses the combined acceleration, velocity and displacement output feedback and works directly on second-order system models without the knowledge of the unassigned eigenpairs. It allows the input and output matrices to be prescribed beforehand in a simple form. The real-valued spectral decomposition of the symmetric quadratic pencil is adopted to derive a homogeneous matrix equation of output feedback gain matrices that assure the no spillover eigenvalue assignment. The method is validated by some illustrative numerical examples.

scholarly journals Disturbance Attenuation via Output Feedback for Nonlinear Time-Delay Systems with Input Matching Uncertainty

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Chao Guo ◽  
Kemei Zhang
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Output Growth ◽  
Disturbance Attenuation ◽  
Delay Systems ◽  
Multiple Time ◽  
Closed Loop System ◽  
Input Matching ◽  
System States ◽  
Dynamic Gain

This paper studies the problem of output feedback disturbance attenuation for a class of uncertain nonlinear systems with input matching uncertainty and unknown multiple time-varying delays, whose nonlinearities are bounded by unmeasured states multiplying unknown polynomial-of-output growth rate. By skillfully combining extended state observer, dynamic gain technique, and Lyapunov-Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain to guarantee the boundedness of closed-loop system states and the achievement of global disturbance attenuation in the L2-gain sense.

scholarly journals Adaptive Output Feedback Stabilization of Nonholonomic Systems with Nonlinear Parameterization

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanling Shang ◽  
Ye Yuan ◽  
Fushun Yuan
Keyword(s):  
Output Feedback ◽  
Design Procedure ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Nonlinear Parameterization ◽  
Output Feedback Stabilization ◽  
Backstepping Approach ◽  
Nonlinearly Parameterized ◽  
System States ◽  
Parameter Separation

This paper investigates the problem of adaptive output feedback stabilization for a class of nonholonomic systems with nonlinear parameterization and strong nonlinear drifts. A parameter separation technique is introduced to transform nonlinearly parameterized system into a linear-like parameterized system. Then, by using the integrator backstepping approach based on observer and parameter estimator, a constructive design procedure for output feedback adaptive control is given. And a switching strategy is developed to eliminate the phenomenon of uncontrollability. It is shown that, under some conditions, the proposed controller can guarantee that all the system states globally converge to the origin, while other signals remain bounded. An illustrative example is also provided to demonstrate the effectiveness of the proposed scheme.

scholarly journals Global Finite-Time Output Feedback Stabilization for a Class of Uncertain Nonholonomic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Baojian Du ◽  
Fangzheng Gao ◽  
Fushun Yuan
Keyword(s):  
Output Feedback ◽  
Finite Time ◽  
Closed Loop ◽  
Output Feedback Control ◽  
Design Procedure ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Closed Loop System ◽  
Output Feedback Stabilization ◽  
Switching Control Strategy

This paper investigates the problem of global finite-time stabilization by output feedback for a class of nonholonomic systems in chained form with uncertainties. By using backstepping recursive technique and the homogeneous domination approach, a constructive design procedure for output feedback control is given. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Sliding mode control revisited

2020 ◽  
Vol 42 (14) ◽  
pp. 2698-2707
Author(s):  
Masoud Bahraini ◽  
Mohammad Javad Yazdanpanah ◽  
Shokufeh Vakili ◽  
Mohammad Reza Jahed-Motlagh
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Sliding Mode ◽  
Design Procedure ◽  
Systematic Design ◽  
Closed Loop System ◽  
Guaranteed Stability ◽  
Sliding Mode Controllers ◽  
Bounded Disturbances ◽  
System States

Controller design for nonlinear systems in its general form is complicated and an open problem. Finding a solution to this problem becomes more complicated when unwanted terms, such as disturbance, are taken into account. To provide a robust design for a subclass of nonlinear systems, sliding mode controllers (SMCs) are used. These controllers have a systematic design procedure and can reject bounded disturbances and at the same time guarantee stability. The guaranteed stability is achieved by separating system states into two parts and assuming that the input to state stability (ISS) condition holds for internal dynamics. This condition restricts the applicability of the SMC and limits the system performance when the controller is designed based on that. In order to remove this restriction and improve the performance, the ISS condition has been relaxed in this study. The relaxation is performed by redesigning SMCs based on suggested Lyapunov functions. The proposed idea insures global asymptotic stability of the closed loop system and is used to revise different well-known SMCs such as conventional SMC, terminal SMC, non-singular terminal SMC, integral SMC, super-twisting SMC, and super-twisting integral SMC. Comparisons between conventional and revised versions are made using simulation to demonstrate excellence of the revisited controllers.

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

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