On approximating the step response of a third-order linear system by a second-order linear system

1968 ◽  
Vol 13 (6) ◽  
pp. 739-739 ◽  
Author(s):  
R. Monzingo
Keyword(s):  
Linear System ◽  
Second Order ◽  
Step Response ◽  
Third Order ◽  
Order Linear

Synthesis and Optimization of Transient Performances for Underdamped Second-Order Linear System Based on the Switching Control Strategy

2012 ◽  
Author(s):  
Qingyu Su ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Linear System ◽  
Control Strategy ◽  
Optimization Problems ◽  
Switching Control ◽  
Second Order ◽  
Order Linear ◽  
Output Response ◽  
Special Cases ◽  
Switching Control Strategy ◽  
The Given

In this paper, the synthesis and optimization problems of the transient performances, such as overshoot and setting time, of the output response with respect to a step signal for an under-damped second-order linear system are studied. The traditional control strategy and the switching control strategy are used, respectively. Our control objective is twofold: Objective 1 is to ensure that the overshoot of the system output does not violate the given safety bound and objective 2 is to ensure that the settling time is smaller than the given allowable time. The obtained results indicate that the switching control strategy has main two evident advantages: firstly, the switching proportional controllers can take advantages of both the quick response and the small overshoot of the output response. Secondly, the switching controller is always available, while the single proportional controller is available in some special cases. Finally, an example of servomotor is given to demonstrate the effectiveness of the proposed method.

Sufficient Conditions for Minimum-Phase Second-Order Linear Systems

1995 ◽  
Vol 1 (2) ◽  
pp. 183-199 ◽  
Author(s):  
Jong-Lick Lin ◽  
Jer-Nan Juang
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Common Knowledge ◽  
Sufficient Conditions ◽  
Second Order ◽  
Geometrical Approach ◽  
Minimum Phase ◽  
Sensors And Actuators ◽  
Influence Matrix ◽  
Order Linear

Several sufficient conditions are derived for a second-order linear system to be minimum phase. It is commonly known that a second-order linear system with collocated sensors and actuators is minimum phase. In general, this common knowledge is correct mathematically when the input influence matrix is the transpose of the output influence matrix. In this paper, we extend this knowledge to the case with noncollocated actuators and sensors. First, a conventional approach is used to prove some sufficient conditions of sensor and actuator locations for a system to be minimum phase. Second, a geometrical approach is introduced to discuss the sufficient conditions, and then used to derive other more useful sufficient conditions for a minimum-phase second-order linear system. Many illustrative examples are provided for the readers to better understand the theories developed in this paper.

Stochastic Resonance in a Second-Order Linear System Subject to Signal-Modulated Noise

2012 ◽  
Vol 538-541 ◽  
pp. 2582-2585 ◽  
Author(s):  
Feng Bao Li ◽  
Xiao Yan Lei ◽  
Fu Cheng Zhu
Keyword(s):  
System Theory ◽  
Linear System ◽  
Stochastic Resonance ◽  
System Parameter ◽  
Second Order ◽  
Order Derivative ◽  
Signal Frequency ◽  
Noise Strength ◽  
Order Linear ◽  
Output Amplitude

An over-damped second-order linear system with fluctuant coefficient of the second-order derivative and signal-modulated noise is considered. Based on linear-system theory, the expression of the output amplitude is obtained. Analytical results shows that the output amplitude is a non-monotonic function of the noise strength, and it varies non-monotonously with the increase of the system parameter a and b, while it decreases monotonously with the increase of the signal frequency and the system parameter c.

scholarly journals ON THE TRANSFORMATION OF THE LINEAR DIFFERENTIAL EQUATION INTO A SYSTEM OF THE FIRST ORDER EQUATIONS

2019 ◽  
pp. 71-75
Author(s):  
M.I. Ayzatsky
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Second Order ◽  
Dimensional System ◽  
Third Order ◽  
Order Linear ◽  
First Order ◽  
The Third ◽  
Linear Differential

The generalization of the transformation of the linear differential equation into a system of the first order equations is presented. The proposed transformation gives possibility to get new forms of the N-dimensional system of first order equations that can be useful for analysis of the solutions of the N-th-order differential equations. In particular, for the third-order linear equation the nonlinear second-order equation that plays the same role as the Riccati equation for second-order linear equation is obtained.

Sign in / Sign up

Export Citation Format

Share Document