Sensitivity Reduction by State Derivative Feedback

1988 ◽  
Vol 110 (1) ◽  
pp. 84-93 ◽  
Author(s):  
A. Haraldsdottir ◽  
P. T. Kabamba ◽  
A. G. Ulsoy
Keyword(s):  
Closed Loop ◽  
Design Procedure ◽  
State Feedback Control ◽  
Original Design ◽  
Stability Robustness ◽  
Sensitivity Indices ◽  
Feedback Control Systems ◽  
Response Amplification ◽  
Time Invariant ◽  
Time Systems

This paper shows that the sensitivity of state feedback control systems can be reduced by additional state derivative feedback, for a fixed closed loop eigenstructure. The price of this sensitivity reduction is in general noise response amplification. Two indices which quantify stability robustness and response sensitivity are given for time invariant continuous time and discrete time systems, together with an index of response to disturbances and noise. Closed form expressions for the gradients of these indices are given. A two step design procedure is proposed which consists of first selecting a closed loop eigenstructure, then minimizing one of the sensitivity indices under a magnitude constraint on the noise response. Examples are given to illustrate this original design procedure.

scholarly journals H∞ control of discrete-time linear systems constrained in state by equality constraints

2012 ◽  
Vol 22 (3) ◽  
pp. 551-560 ◽  
Author(s):  
Anna Filasová ◽  
Dušan Krokavec
Keyword(s):  
Discrete Time ◽  
Design Procedure ◽  
Equality Constraints ◽  
State Feedback Control ◽  
Computation Method ◽  
Control Law ◽  
State Variables ◽  
Bounded Real Lemma ◽  
Time Systems ◽  
Time Linear

Abstract In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outperforms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.

Design of Reset Control Systems: The PI + CI Compensator

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Alfonso Baños ◽  
Angel Vidal
Keyword(s):  
Control Systems ◽  
Dynamic Systems ◽  
Closed Loop ◽  
Dead Time ◽  
Nonlinear Characteristic ◽  
Integral Term ◽  
Wide Range ◽  
Reset Control ◽  
Time Invariant ◽  
Time Systems

Reset compensation has been used to overcome limitations of linear and time invariant (LTI) compensation. In this work, a new reset compensator, referred to as proportional and integral (PI) + CI (Clegg integrator), is introduced. It basically consists of adding a Clegg integrator to a PI compensator, with the goal of improving the closed loop response by using the nonlinear characteristic of this element. It turns out that by resetting a percentage of the integral term in a PI compensator, a significant improvement can be obtained over a well-tuned PI compensator in some relevant practical cases, such as systems with dominant lag and integrating systems. The work is devoted to the development of PI + CI tuning rules for basic dynamic systems in a wide range of applications, including first and higher order plus dead time systems.

On Passive Implementation of Feedback Control Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 339-342
Author(s):  
R. Shoureshi
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
State Feedback ◽  
Closed Loop ◽  
State Feedback Control ◽  
Closed Loop Control ◽  
Linear Quadratic ◽  
Loop Control ◽  
Feedback Control Systems ◽  
Linear Quadratic Regulators

Closed-loop control systems, especially linear quadratic regulators (LQR), require feedbacks of all states. This requirement may not be feasible for those systems which have limitations due to geometry, power, required sensors, size, and cost. To overcome such requirements a passive method for implementation of state feedback control systems is presented.

On sensor quantization in linear control systems: Krasovskii solutions meet semidefinite programming

2019 ◽  
Vol 37 (2) ◽  
pp. 395-417 ◽  
Author(s):  
Francesco Ferrante ◽  
Frédéric Gouaisbaut ◽  
Sophie Tarbouriech
Keyword(s):  
Control Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Loop System ◽  
State Feedback Control ◽  
Linear Control Systems ◽  
Compact Set ◽  
Closed Loop System ◽  
Feedback Control Systems ◽  
Linear State

Abstract Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions (to the closed-loop system) are considered. Sufficient conditions in the form of matrix inequalities are proposed to characterize uniform global asymptotic stability of a compact set containing the origin. Such conditions are shown to be always feasible whenever the quantization-free closed-loop system is asymptotically stable. Building on the obtained conditions, computationally affordable algorithms for the solution to the considered problems are illustrated. The effectiveness of the proposed methodology is shown in three examples.

scholarly journals Observer-Based Mixedℋ2/ℋ∞Tracking Control for Continuous-Time Systems with Integral Action and Pole Placement

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Huxiong Li
Keyword(s):  
Continuous Time ◽  
Tracking Control ◽  
Closed Loop ◽  
State Feedback Control ◽  
Pole Placement ◽  
Linear Matrix ◽  
Closed Loop Systems ◽  
Integral Action ◽  
Continuous Time Systems ◽  
Time Systems

The tracking problem for continuous-time systems is investigated. It is assumed that the states of the systems are not available. An observer is firstly designed to estimate the states by using theℋ∞method. The control action is consist of a state-feedback control, an integral component, and a feedforward loop. The linear-matrix-inequality region is used to constrain the eigenvalue location for the closed-loop systems. The control gains can be obtained by solving a sequence of linear matrix inequalities (LMIs) which can guarantee the mixedℋ2/ℋ∞performance for the closed-loop systems.

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.

Decentralized H ∞ control for damping power system oscillations

2012 ◽  
Vol 2 (1) ◽  
Author(s):  
Guo-Jie Li ◽  
Tek Lie
Keyword(s):  
Power Systems ◽  
Power System ◽  
Large Scale ◽  
Digital Simulation ◽  
Design Procedure ◽  
Disturbance Attenuation ◽  
System Stability ◽  
Frequency Noise ◽  
Stability Robustness ◽  
Norm Bound

AbstractInter-area oscillations are serious problems to large-scale power systems. A decentralized H ∞ generator excitation controller of a power system is proposed to damp the inter-area oscillations and to enhance power system stability. The design procedure for a linear composite system is presented in terms of positive semi-definite solutions to modified algebraic inequalities. The resulting controller guarantees closed-loop stability, robustness and an H ∞-norm bound on disturbance attenuation even under uncertainties such as high frequency noise. The control is decentralized in the sense that the control of each generator depends on local information only. The effectiveness of the H ∞ controller is demonstrated through digital simulation studies on a two-machine power system.

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