Browsing by Author "Liaw, DC"

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A bifurcation study of vehicle's steering dynamics
(2005)
Liaw, DC
;
Chiang, HH
;
Lee, TT
;
電控工程研究所
;
Institute of Electrical and Control Engineering
Issues of stability and bifurcation phenomena in vehicle's steering dynamics are presented. Based on the assumption of constant driving speed, a second order nonlinear lateral dynamical model is obtained. Local stability and existence conditions for saddle node bifurcation appearing in vehicle dynamics with respect to the variation of the front wheel steering angle are then derived via system linearization and local bifurcation analysis. Bifurcation phenomena occurring in nonlinear vehicle lateral dynamics might result in spin and/or system instability. Perturbation method is employed to solve for an approximation of system equilibrium near the zero value of the front wheel steering angle, which reveals the relationship between sideslip angle and the applied front wheel angle. Numerical study of a simple example verifies the theoretical analysis.
A general invariance principle for nonlinear time-varying systems and its applications
(2001-12-01)
Lee, TC
;
Liaw, DC
;
Chen, BS
;
電控工程研究所
;
Institute of Electrical and Control Engineering
A general invariance principle, from the output-to-state point of view, is proposed for the dynamical analysis of nonlinear time-varying systems. This is achieved by the construction of a simple and intuitive criterion using integral inequality of the output function and modified detectability conditions. The proposed scheme can be viewed as an extension of the integral invariance principle (Byrnes and Martin, 1995) for time-invariant systems to time-varying systems. Such extension is nontrivial and can be used in various research areas such as adaptive control, tracking control and the control of driftless systems. An application to global tracking control of four-wheeled mobile robots is given to demonstrate the feasibility and validity of the proposed approach.
Analysis of longitudinal flight dynamics: A bifurcation-theoretic approach
(2001-01-01)
Liaw, DC
;
Song, CC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
Bifurcation theory has been used to study the nonlinear dynamics and stability of many modern aircraft, especially in broad angle-of-attack flight dynamics. However, the main application of bifurcation analysis is based on numerical simulations to predict and explain the nonlinear instability of flight dynamics by the use of parametric continuation methods. Bifurcation theory is applied to theoretically analyze the nonlinear phenomena of longitudinal flight dynamics, by the choice of the elevator deflection and mass of the aircraft as system parameters. Both stationary and Hopf bifurcations may appear at some critical values of elevator command. Discontinuity also may occur at system equilibria as system parameters vary. The bifurcation phenomena occurring in nonlinear aircraft dynamics might result in jump behaviors, pitch oscillations, or system instabilities. Numerical study of a simple third-order model of longitudinal dynamics verifies the theoretical analysis. Qualitative results are obtained to understand the longitudinal flight dynamics.
Application of center manifold reduction to nonlinear system stabilization
(1998-05-01)
Liaw, DC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
The Center Manifold Theorem is applied to the local feedback stabilization of nonlinear systems in critical cases. The paper addresses two particular critical cases of which the system linearization at the equilibrium point of interest is assumed to possess either a simple zero eigenvalue or a complex conjugate pair of simple and pure imaginary eigenvalues. In either case, the noncritical eigenvalues are taken to be stable. The results on stabilizability and stabilization are given explicitly in terms of the nonlinear model of interest in its original form, i.e., before reduction to the center manifold. Moreover, the formulation given in this paper uncovers connections between results obtained using the center manifold reduction and those of an alternative approach. (C) 1998 Elsevier Science Inc. All rights reserved.
Application of FIDF to the detection of unstable behaviors in compression systems
(2000)
Liang, YW
;
Liaw, DC
;
Wu, YC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
Issues concerning the detection of surge and rotating stall in a compression system are studied in this paper. It is observed that the plenum pressure rise and mass flow rate of a compression system exhibit abrupt change due to the appearance of surge or rotating stall, while those of it's linearized model do not. With this observation, a linear-based fault identification filter (FIDF) design technique is proposed to detect these two instabilities. This is achieved by treating the difference between the output of the compression system and that of its linearized model at an unstalled operating point as a fault vector and then investigating the effect of the fault on the designed FIDF. Simulation results for Moore and Greitzer's compression model [14] are given to demonstrate the effectiveness of the proposed scheme. The study may provide a means of detecting the occurrence of unstable phenomena at the onset so that a corrective action can be made.
Application of VSC reliable design to spacecraft attitude tracking
(2005)
Liang, YW
;
Xu, SD
;
Chu, TC
;
Cheng, CC
;
Liaw, DC
This study investigates variable structure reliable control issues of nonlinear systems and its applications to spacecraft attitude tracking problems. The proposed passive reliable control laws must know in advance which group of actuators is allowed to fail. These reliable controllers need not the solution of Hamilton-Jacobi (HJ) equation or inequality that are essentials in optimal approaches such as LQR and Hoo reliable designs. As a matter of fact, this approach is able to relax the computational load in computing the solution of HJ equation. The proposed reliable designs are also applied to spacecraft attitude tracking problems to explain their effectiveness and benefits. Finally, simulation results and comparisons between LQR and Variable Structure Control (VSC) reliable designs are presented to illustrate the merits of the proposed scheme. Although the proposed design is a passive one, it may provide a guideline for active design when a Fault Detection and Diagnosis (FDD) scheme is available.
Asymptotic stabilization of driftless systems
(1999-02-15)
Liaw, DC
;
Liang, YW
;
電控工程研究所
;
Institute of Electrical and Control Engineering
Issues of asymptotic stabilization of a class of non-linear driftless systems are presented. In addition to the necessary and sufficient condition for the existence of a smooth time-invariant asymptotic stabilizer, sufficient condition for the existence of a quadratic-type Lyapunov function candidate is also proposed herein to alleviate the construction of stabilizing control laws. Following the deduction of the equivalence of the sufficient condition and the determination of the local definiteness of a defined scalar function, the stabilizability checking conditions are then derived in terms of system dynamics and its derivatives at the origin only. These are achieved by taking Taylor's series expansion on system dynamics. The derived conditions are shown to be consistent with those obtained by Brockett. Comparative results of Liaw and Liang are also included. Finally, examples are given to demonstrate the use of the main results.
Bifurcation analysis of power systems with tap changer
(2005)
Liaw, DC
;
Fang, KH
;
Song, CC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
A bifurcation analysis of nonlinear dynamics for electric power system with tap changer is presented in this paper. Based on a model of electric power system proposed by Dobson and Chiang (1988) with one extra tap changer added parallel to the local nonlinear power load, the saddle-node bifurcation and Hopf bifurcations are observed by treating the real power, reactive power and tap changer as system parameters. The occurrences of subcritical Hopf bifurcation and saddle-node bifurcation lead to the appearance of dynamic and static voltage collapses, respectively. These phenomena may generate the progressive decrease in voltage magnitude in electric power system.
Contact friction compensation for robots using genetic learning algorithms
(1998-10-01)
Liaw, DC
;
Huang, JT
;
電控工程研究所
;
Institute of Electrical and Control Engineering
In this paper, the issues of contact friction compensation for constrained robots are presented. The proposed design consists of two loops. The inner loop is for the inverse dynamics control which linearizes the system by canceling nonlinear dynamics, while the outer loop is for friction compensation. Although various models of friction have been proposed in many engineering applications, frictional force can be modeled by the Coulomb friction pins the viscous force. Based on such a model, an on-line genetic algorithm is proposed to learn the friction coefficients for friction model. The friction compensation control input is also implemented in terms of the friction coefficients to cancel the effect of unknown friction. By the guidance of the fitness function, the genetic learning algorithm searches for the best-fit value in a way like the natural surviving laws. Simulation results demonstrate that the proposed on-line genetic algorithm can achieve good friction compensation even under the conditions of measurement noise and system uncertainty. Moreover, the proposed control scheme is also found to be feasible for friction compensation of friction model with Stribeck effect and position-dependent friction model.
Contact friction compensation for robots using genetic learning algorithms
(1998-10-01)
Liaw, DC
;
Huang, JT
;
電控工程研究所
;
Institute of Electrical and Control Engineering
In this paper, the issues of contact friction compensation for constrained robots are presented. The proposed design consists of two loops. The inner loop is for the inverse dynamics control which linearizes the system by canceling nonlinear dynamics, while the outer loop is for friction compensation. Although various models of friction have been proposed in many engineering applications, frictional force can be modeled by the Coulomb friction pins the viscous force. Based on such a model, an on-line genetic algorithm is proposed to learn the friction coefficients for friction model. The friction compensation control input is also implemented in terms of the friction coefficients to cancel the effect of unknown friction. By the guidance of the fitness function, the genetic learning algorithm searches for the best-fit value in a way like the natural surviving laws. Simulation results demonstrate that the proposed on-line genetic algorithm can achieve good friction compensation even under the conditions of measurement noise and system uncertainty. Moreover, the proposed control scheme is also found to be feasible for friction compensation of friction model with Stribeck effect and position-dependent friction model.
Detection of surge and stall in compression systems: An example study
(2001-10-01)
Liang, YW
;
Liaw, DC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
Issues concerning the detection of surge and rotating stall in a compression system are considered. It is observed that, when surge or rotating stall happens, the plenum pressure rise and mass flow rate of a compression system exhibit abrupt change while those of its linearized model do not. With this observation, it is shown that the surge and rotating stall can be successfully detected by employing a linear-based fault identification filter (FIDF) design technique. This is achieved by treating the difference between the output of the compression system and that of its linearized model at an unstalled operating point as a fault vector and then investigating the effect of the fault on the designed FIDE Simulation results with regard to Moore and Greitzer's compression model (1986) are given to demonstrate the effectiveness of the proposed approach. The theoretical study presented in this note may provide a guideline of detecting the occurrence of unstable phenomena at the onset so that corrective responses can be made in the practical applications.
Feedback stabilization of nonlinear driftless systems with applications to homogeneous-type systems
(1997-02-01)
Liaw, DC
;
Liang, YW
;
電控工程研究所
;
Institute of Electrical and Control Engineering
Issues of asymptotic stabilization of nonlinear driftless systems as given by x = g(x)u with applications to homogeneous-type driftless systems are presented. Conditions of the existence of a smooth time-invariant stabilizer for general nonlinear driftless systems are obtained by the construction of quadratic-type Lyapunov functions. The proposed conditions do not contradict Brockett's (1983) result for the existence of a smooth time-invariant stabilizer. These results are then employed to study the stabilization problem of homogeneous-type systems. Sufficient conditions are obtained for the stabilization of planar type homogeneous driftless systems with positive order. It is shown that the single input control driftless systems cannot be asymptotically stabilizable by any continuous control if g(x) is a homogeneous function of even order. Moreover, equivalent conditions for the stabilizability of linear driftless systems and the explicit design of stabilizing control laws for bilinear driftless systems are also presented.
Feedback stabilization of nonlinear driftless systems with applications to homogeneous-type systems
(1997-02-01)
Liaw, DC
;
Liang, YW
;
交大名義發表
;
電控工程研究所
;
National Chiao Tung University
Issues of asymptotic stabilization of nonlinear driftless systems as given by x = g(x)u with applications to homogeneous-type driftless systems are presented. Conditions of the existence of a smooth time-invariant stabilizer for general nonlinear driftless systems are obtained by the construction of quadratic-type Lyapunov functions. The proposed conditions do not contradict Brockett's (1983) result for the existence of a smooth time-invariant stabilizer. These results are then employed to study the stabilization problem of homogeneous-type systems. Sufficient conditions are obtained for the stabilization of planar type homogeneous driftless systems with positive order. It is shown that the single input control driftless systems cannot be asymptotically stabilizable by any continuous control if g(x) is a homogeneous function of even order. Moreover, equivalent conditions for the stabilizability of linear driftless systems and the explicit design of stabilizing control laws for bilinear driftless systems are also presented.
Global stabilization of axial compressors using nonlinear cancellation and backstepping designs
(1998-12-01)
Liaw, DC
;
Huang, JT
;
電控工程研究所
;
Institute of Electrical and Control Engineering
Issues concerning the global stabilization of axial compressors are presented Instead of locally stabilizing the bifurcated rotating stall equilibria to avoid suddern performance drop, control schemes are proposed to globally stabilize the unstalled nominal operating paints. These are achieved by employing nonlinear cancellation and backstepping designs via either throttle or direct mass flow rate control if the compressor characteristic satisfies the 'left-tilt' property. The designs not only guarantee a safe operation close to the maximum achievable pressure rise, but the bifurcated system equilibria are also found to be stabilized due to the elimination of the jump phenomenon. Though both throttle and direct mass flow rate control schemes can be implemented for global stabilization, numerical simulations demonstrate that direct mass flow rate control achieves better post-stall system behaviour.
Identification and compensation of target's maneuver in missile guidance via genetic algorithms approach
(2003)
Liaw, DC
;
Weng, HL
;
電控工程研究所
;
Institute of Electrical and Control Engineering
In this paper, a two-loop control scheme is proposed for the identification and compensation of homing missile guidance. The inner-loop adopts the realistic true proportional navigation design (Yang and Yang,1996) for missile guidance without considering the target's maneuver, while the outer-loop is to construct a genetic algorithm for identifying and cancelling the target's maneuver. Although the target's maneuver may have various types of motion, an on-line genetic algorithm is proposed to learn the target's maneuvering behavior which can be any piecewise continuous function. A compensation control scheme is also implemented to simultaneously cancel the effect of such unknown maneuver. Simulation results demonstrate that the proposed on-line genetic algorithm base control law can achieve good maneuver compensation even under the conditions with measurement noise. Moreover, the coefficients of maneuver are found to be decided exactly if the maneuvering function is predictable.
Nonlinear control for missile terminal guidance
(2000-12-01)
Liaw, DC
;
Liang, YW
;
Cheng, CC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
Variable Structure Control (VSC) technique is applied to the design of robust homing missile guidance laws. In the design procedure, the target's maneuver is assumed to be unpredictable and is considered as disturbances. Guidance laws are then proposed to achieve the interception performance for both cases of longitude-axis control being available and unavailable. The proposed guidance laws are continuous which alleviate chattering drawback by classic VSC design. Results are obtained and compared with those by realistic true proportional navigation design to illustrate the benefits of the proposed decision. [S0022-0434(00)00604-3].
Nonlinear control of longitudinal flight dynamics
(2003)
Liaw, DC
;
Song, CC
;
Chung, WC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
This paper presents the nonlinear analysis and control of a third-order model for longitudinal flight dynamics. Bifurcation analysis using numerical study for F-8 aircraft reveals that Hopf bifurcations may occur at some critical values of the elevator commands. These results agree with the well-known nonlinear phenomena existed in longitudinal flight dynamics. Furthermore, bifurcation control using both washout filter and direct state feedback are applied to develop the stabilizing laws for system equilibria and periodic solutions emerged from bifurcation points. Numerical simulations are provided to demonstrate these main results.
On asymptotic stabilization of driftless systems
(2000-09-11)
Liang, YW
;
Liaw, DC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
A simple approach is proposed to investigate the stabilization of driftless systems. By taking the control input as a function of system states, we can transform the stabilization design into a stability problem. The known stability results on the nonlinear autonomous system are then employed to derive the asymptotically stabilizing controllers by solving an algebraic equation. Existence conditions of the asymptotic stabilizing feedback controller for the driftless systems by employing the stability criteria on linear systems and a class of third-order homogeneous systems are obtained to demonstrate the application of the approach. (C) 2000 Elsevier Science Inc. All rights reserved.
Parametric study of a resonant switched capacitor DC-DC converter
(2001)
Lin, YC
;
Liaw, DC
;
電控工程研究所
;
Institute of Electrical and Control Engineering
The zero-current switching resonant switched capacitor DC-DC converter is a new type of power converter, which has features of low weight; small volume, high efficiency, low EMI and feasibility of fabrication on a semiconductor IC chip. In this study, we focus on the parametric analysis of a double-mode resonant switched capacitor converter proposed by Cheng in 1998. Since there exists great performance differences between ideal model and real circuit, in this work we propose a modified model by adding the resistance of circuit components. The modified model is then employed to study the circuit performance with respect to the loading effect and the variation of circuit parameters. Simulation results were found to be nearly in accordance with Cheng's experiment. In the paper, the average output voltage is explicitly expressed in terms of the so-called live time ratio, which provides a means of regulating the converter's output voltage.
Quadratic polynomial solutions of the Hamilton-Jacobi inequality in reliable control design
(1998-09-01)
Liaw, DC
;
Liang, YW
;
電控工程研究所
;
Institute of Electrical and Control Engineering
In the design of nonlinear reliable controllers, one major issue is to solve for the solutions of the Hamilton-Jacobi inequality. In general, it is hard to obtain a closed form solutions due to the nonlinear nature of the inequality. In this paper, we seek for the existence conditions of quadratic type positive semidefinite solutions of Hamilton-Jacobi inequality. This is achieved by taking Taylor's series expansion of system dynamics and investigating the negative definiteness of the associated Hamilton up to fourth order. An algorithm is proposed to seek for possible solutions. The candidate of solution is firstly determined from the associated algebraic Riccati inequality. The solution is then obtained from the candidate which makes the the truncated fourth order polynomial of the inequality to be locally negative definite. Existence conditions of the solution are explicitly attained for the cases of which system linearization possesses one uncontrollable zero eigenvalue and a pair of pure imaginary uncontrollable eigenvalues. An example is given to demonstrate the application to reliable control design problem.