scholarly journals Control of Linear Time-Varying Systems Using Forward Riccati Equation

1997 ◽  
Vol 119 (3) ◽  
pp. 536-540 ◽  
Author(s):  
Min-Shin Chen ◽  
Chung-yao Kao
Keyword(s):  
Boundary Condition ◽  
Riccati Equation ◽  
State Feedback ◽  
Linear Time ◽  
The State ◽  
State Feedback Control ◽  
Feedback Gain ◽  
Time Varying ◽  
Time Varying Systems ◽  
Future Information

This paper presents a new state feedback control design for linear time-varying systems. In conventional control designs such as the LQ optimal control, the state feedback gain is calculated off-line by solving a Differential Riccati Equation (DRE) backwards with the boundary condition set at some future time. The apparent disad-vantage of using a backward DRE is that future information of the system matrices is required to find the state feedback gain at every time instant. In this paper, an inversion state transformation is applied to the system so that the DRE associated with the transformed system becomes forward in the sense that its boundary condition is set at the initial time of operation (t = t0). As a result, the forward DRE can be calculated on-line without using future information of the system matrices.

Stabilization of linear time-varying systems using proportional-derivative state feedback

2017 ◽  
Vol 40 (7) ◽  
pp. 2100-2115 ◽  
Author(s):  
Taha HS Abdelaziz
Keyword(s):  
Degrees Of Freedom ◽  
State Feedback ◽  
Linear Time ◽  
State Feedback Control ◽  
Time Varying ◽  
Closed Loop Systems ◽  
Continuous Time Systems ◽  
Time Varying Systems ◽  
Small Gain ◽  
Time Systems

This paper presents the stabilization approach for linear time-varying continuous-time systems using proportional-derivative (PD) state feedback control. The solvability conditions for the problem are considered. The general analytical expressions for the PD controller gains are derived, which describe the available degrees of freedom offered by PD state feedback. The non-uniqueness of the controller gains is utilized to obtain closed-loop systems with small gain elements. Two numerical examples are introduced to demonstrate the effectiveness of the proposed approach.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Desain Power System Stabilizer Berbasis Fuzzy dan Particle Swarm Optimization

2019 ◽  
Vol 10 (1) ◽  
pp. 1-8
Author(s):  
Tamaji
Keyword(s):  
Particle Swarm Optimization ◽  
Feedback Control ◽  
Power System ◽  
State Feedback ◽  
The State ◽  
State Feedback Control ◽  
Power System Stabilizer ◽  
Feedback Gain ◽  
Swarm Optimization ◽  
System Stabilizer

One important factor to produce  a qualified electricity is the stability of the system.  An unstable system resulted  an undamped oscilation of system, and the stable system can damp the oscilation quickly. Therefore, it is necessary to apply  a stability device to a power system and it is called a Power System Stabilizer (PSS). One of stability design is a feedback control design. Here, in this research, the state feedback control are designed for Single Machine Infinite Bus (SMIB) . The SMIB model is non linear therefore the feedback control can’t be designed directly. Some researchers do linearize the system before design the feedback control.  In this research, a nonlinear model of SMIB is build in a state space form. Subsequently, a fuzzification Takagi-Sugeno is applied. The state feedback controls are applied to design the control of SMIB fuzzy system, a state feedback gain is determined using method Routh Hurwitz. The determining the parameter of state feedback gain influence the performance of SMIB. Therefore, it is important to determine the suitable parameter such that the SMIB has the optimal performance. The Particle Swarm Optimization (PSO) is applied to optimaze the performance of SMIB. In these research, it is compared the performance of SMIB by applying between Routh Hurwitz, fuzzy Routh Hurwitz, PSO fuzzy Routh Hurwitz for state feedback control. The simulation result show that Performance of SMIB using The PSO Fuzzy Routh  Hurwitz state feedback can improve the performance of SMIB, but the performance of Efd become oscillate and this method influence by the chosen parameter.

State Feedback and Output Feedback Control of Polynomial Nonlinear Systems Using Fractional Lyapunov Functions

2007 ◽  
Author(s):  
Qian Zheng ◽  
Fen Wu
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Output Feedback ◽  
Lyapunov Functions ◽  
State Feedback ◽  
The State ◽  
State Feedback Control ◽  
Feedback Gain ◽  
Variation Rate

In this paper, we will study the state feedback control problem of polynomial nonlinear systems using fractional Lyapunov functions. By adding constraints to bound the variation rate of each state, the general difficulty of calculating derivative of nonquadratic Lyapunov function is effectively overcome. As a result, the state feedback conditions are simplified as a set of Linear Matrix Inequalities (LMIs) with polynomial entries. Computationally tractable solution is obtained by Sum-of-Squares (SOS) decomposition. And it turns out that both of the Lyapunov matrix and the state feedback gain are state dependent fractional matrix functions, where the numerator as well as the denominator can be polynomials with flexible forms and higher nonlinearities involved in. Same idea is extended to a class of output dependent nonlinear systems and the stabilizing output feedback controller is specified as polynomial of output. Synthesis conditions are similarly derived as using constant Lyapunov function except that all entries in LMIs are polynomials of output with derivative of output involved in. By bounding the variation rate of output and gridding on the bounded interval, the LMIs are solvable by SOS decomposition. Finally, two examples are used to materialize the design scheme and clarify the various choices on state boundaries.

scholarly journals Robust H∞ stabilisation with definite attenuance of an uncertain impulsive switche system

2005 ◽  
Vol 46 (4) ◽  
pp. 471-484 ◽  
Author(s):  
Honglei Xu ◽  
Xinzhi Liu ◽  
Kok Lay Teo
Keyword(s):  
Feedback Control ◽  
Switched Systems ◽  
State Feedback ◽  
The State ◽  
State Feedback Control ◽  
State Model ◽  
Control Law ◽  
Time Varying ◽  
Impulsive Switched Systems ◽  
Bounded Uncertainty

AbstractIn this paper, we study the problem of robust H∞ stabilisation with definite attenuance for a class of impulsive switched systems with time-varying uncertainty. A norm-bounded uncertainty is assumed to appear in all the matrices of the state model. An LMI-based method for robust· H∞ stabilisation with definite attenuance via a state feedback control law is developed. A simulation example is presented to demonstrate the effectiveness of the proposed method.

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