Hung-I Chin

Limit cycle analysis of nonlinear sampled-data systems by gain-phase margin approach

This work analyzes the limit cycle phenomena of nonlinear sampled-data systems by applying the methods of gain–phase margin testing, the M-locus and the parameter plane. First, a sampled-data control system with nonlinear elements is linearized by the classical method of describing functions. The stability of the equivalent linearized system is then analyzed using the stability equations and the parameter plane method, with adjustable parameters. After the gain–phase margin tester has been added to the forward open-loop system, exactly how the gain–phase margin and the characteristics of the limit cycle are related can be elicited by determining the intersections of the M-locus and the constant gain and phase boundaries. A concise method is presented to solve this problem. The minimum gain–phase margin of the nonlinear sampled-data system at which a limit cycle can occur is investigated. This work indicates that the procedure can be easily extended to analyze the limit cycles of a sampled-data system from a continuous-data system cases considered in the literature. Finally, a sampled-data system with multiple nonlinearities is illustrated to verify the validity of the procedure.

Gain-phase margin analysis of dynamic fuzzy control systems

In this paper, we apply some effective methods, including the gain-phase margin tester, describing function and parameter plane, to predict the limit cycles of dynamic fuzzy control systems with adjustable parameters. Both continuous-time and sampled-data fuzzy control systems are considered. In general, fuzzy control systems are nonlinear. By use of the classical method of describing functions, the dynamic fuzzy controller may be linearized first. According to the stability equations and parameter plane methods, the stability of the equivalent linearized system with adjustable parameters is then analyzed. In addition, a simple approach is also proposed to determine the gain margin and phase margin which limit cycles can occur for robustness. Two examples of continuous-time fuzzy control systems with and without nonlinearity are presented to demonstrate the design procedure. Finally, this approach is also extended to a sampled-data fuzzy control system.

Absolute stability analysis in uncertain static fuzzy control systems with the parametric robust Popov criterion

This study analyzes the absolute stability in static fuzzy logic control systems with certain and uncertain parameters. For certain static fuzzy control systems, the absolute stability can be analyzed with Popov criterion. The uncertain parameters for absolute stability analysis include the reference input, actuator gain and interval linear plant. The parametric robust Popov criterion based on Lurpsilae systems is applied to stability analysis respect to uncertain parameters. In our work, the parametric robust Popov criterion is applied to analyze absolute stability in static fuzzy logic control systems first time. This study can provide a valuable reference in designing fuzzy control systems. Finally, numerical simulations are provided to verify the analytical results.

Limit cycle analysis of uncertain fuzzy vehicle control systems

In this paper, some useful frequency domain methods including describing function, parameter space and Kharitonov approach are applied to analyze the stability of a fuzzy vehicle control system for limit cycle prediction. A systematic procedure is proposed to solve this problem. In general, fuzzy control systems are nonlinear systems. The fuzzy controller can be linearized by the use of classical describing function firstly. By doing so, it is feasible to treat the stability problem of fuzzy control systems as linear one. In order to consider the robustness of the fuzzy vehicle control system, parameter space method and Kharitonov approach are then employed for plotting the stability boundaries. Furthermore, the effect of transport delay is also addressed. Much information of limit cycles can be obtained by this approach. Our work shows that the limit cycles caused by a fuzzy controller can be easily suppressed if the system parameters are chosen carefully.

Robust Control Design for Perturbed Systems by Frequency Domain Approach

This paper is concentrated on a perturbed vehicle control system whose gain margin (GM) and phase margin (PM) are analyzed and for which a novel controller design method satisfying the given specifications on GM, PM, and sensitivity is developed. The approach is applied to the plants with uncertain parameters that vary in intervals. Based on the parameter space method and robust stability criteria, gain and phase boundary curves are generated from the characteristic polynomial of the system with which a gain-phase tester is included in series to perform system stability analysis and controller design. The main concern in the controller design is to find a region in the controller coefficient plane so that the performance of the uncertain system satisfies given specifications. The proposed method is applied to an example of a bus system. Simulation results are given for illustration to show the system performances on GM and PM, and the desired controller meeting the specified conditions in frequency domain for the perturbed system is derived.

Stability Analysis of Equilibrium Points in Static Fuzzy Control Systems with Reference Inputs and Adjustable Parameters

In this paper, the stability in static fuzzy control systems for linear systems with different fixed reference inputs and adjustable parameters are analyzed. Under certain conditions, the unique equilibriums of error in fuzzy control systems can be solved with fixed reference. Furthermore, when the unique equilibrium is stable, the steady state error can be obtained from this stable equilibrium. Under the adjustable parameters and reference inputs, the equilibriums may have stable and unstable transformations each other respect to absolutely stability. Additionally, the insight mechanism for oscillation of equilibrium is also given with a numerical example.

Gain-phase margin analysis of perturbed vehicle control systems

The paper presented here is concentrated on the subject of gain-phase margin (GM and PM) analysis in the frequency domain for perturbed vehicle control systems. The stability of a vehicle control system with perturbed parameters is analyzed by using the parameter space method and stability equations. The coefficients of a characteristic polynomial depend on some uncertain parameters. Determine whether the roots of the perturbed system are in the left-half part of the complex plane and satisfies the conditions under GM and PM constraints. These conditions can be tested graphically in 2 or 3 dimensional parameter space. The necessary and sufficient condition for stability with perturbed parameters within an operating region in the parameter space is that it contains at least one stable point and is not intersected with the image of the jw-axis in the complex plane. The proposed method is applied to an example of a bus system and simulation results are given for illustration to show the PM and GM performances.

Robust Longitudinal Controller and Observer Design for Vehicles with a Riccati Equation Approach

In this paper, the robust stabilizer with Riccati equations is applied to vehicle longitudinal system design. In our design, even if the uncertainties exist in vehicle systems, the designed observer and state feedback controller can stabilize the systems for any given initial conditions. In this method, Riccati equations are solved for finding positive-definite symmetry matrices to construct the observer and state feedback gain matrices. After the inter loop is stable, the PI controller is designed in outer loop for improving the ability of tracking performance. Finally, the simulation shows the feasibility of our design

Stability analysis of a robust fuzzy vehicle steering control system

The main purpose of this paper is to analyze the stability for a fuzzy vehicle steering control system. In general, fuzzy control system is a nonlinear control system. Therefore, the fuzzy controller may be linearized by the use of describing function first. After then, the traditional frequency domain method i.e. parameter plane, is then applied to determine the condition of stability when the system has perturbed or adjustable parameters. A systematic procedure is proposed to solve this problem. The stability problem under the effects of plant parameters and control factors are both considered here. Furthermore, the effect of transport delay is also addressed. The limit cycles provided by a static fuzzy controller can be easily suppressed if the system parameters are chosen properly. Simulation results show the efficiency of our approach.