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.

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.

Desain Power System Stabilizer Berbasis Fuzzy dan Particle Swarm Optimization

2019 ◽  
Vol 10 (1) ◽  
pp. 1-8
Author(s):  
Tamaji 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 qualified electricity is the stability of the system.  An unstable system resulted in 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 is 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. 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 optimize the performance of SMIB. In this research, it is compared to the performance of SMIB by applying between Routh Hurwitz, fuzzy Routh Hurwitz, PSO fuzzy Routh Hurwitz for state feedback control. The simulation result shows 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 influenced by the chosen parameter

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