Integration of PSO and GA for optimum design of fuzzy PID controllers in a pendubot system

In this paper, a novel auto-tuning method is proposed to design fuzzy PID controllers for asymptotical stabilization of a pendubot system. In the proposed method, a fuzzy PID controller is expressed in terms of fuzzy rules, in which the input variables are the error signals and their derivatives, while the output variables are the PID gains. In this manner, the PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than the conventional ones with fixed gains. To tune the fuzzy PID controller simultaneously, an evolutionary learning algorithm integrating particle swarm optimization (PSO) and genetic algorithm (GA) methods is proposed. The simulation results illustrate that the proposed method is indeed more efficient in improving the asymptotical stability of the pendubot system. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Parameter estimation of chaotic systems by a nonlinear time-varying evolution PSO method

An important issue in nonlinear science is parameter estimation for Lorenz chaotic systems. There has been increasing interest in this issue in various research fields, and it could essentially be formulated as a multidimensional optimization problem. A novel evolutionary computation algorithm, nonlinear time-varying evolution particle swarm optimization (NTVEPSO), is employed to estimate these parameters. In the NTVEPSO method, the nonlinear time-varying evolution functions are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments would have an effect that approximates tothe full factorial experiments. The NTVEPSO method and other PSO methods are then applied to identify the Lorenz chaotic system. Simulation results demonstrate the feasibility and superiority of the proposed NTVEPSO method.     

A parameter set division and switching gain-scheduling controllers design method for time-varying plants

This paper presents a new technique to design switching gain-scheduling controllers for plants with measurable time-varying parameters. By dividing the parameter set into a sufficient number of subsets, and by designing a robust controller to each subset, the designed switching gain-scheduling controllers achieve a desired L₂-gain performance for each subset, while ensuring stability whenever a controller switching occurs due to the crossing of the time-varying parameters between any two adjacent subsets. Based on integral quadratic constraints theory and Lyapunov stability theory, a switching gain-scheduling controllers design problem amounts to solving optimization problems. Each optimization problem is to be solved by a combination of the bisection search and the numerical nonsmooth optimization method. The main advantage of the proposed technique is that the division of the parameter region is determined automatically, without any prespecified parameter set division which is required in most of previously developed switching gain-scheduling controllers design methods. A numerical example illustrates the validity of the proposed technique.     

A new class of nonlinear PID controllers with robotic applications

This paper introduces a new class of simple nonlinear PID controllers and provides a formal treatment of their stability analysis. These controllers are comprised of a sector-bounded nonlinear gain in cascade with a linear fixed-gain P, PD, PI, or PID controller. Three simple nonlinear gains are proposed: the sigmoidal function, the hyperbolic function, and the piecewise–linear function. The systems to be controlled are assumed to be modeled or approximated by second-order transfer functions, which can represent many robotic applications. The stability of the closed-loop systems incorporating nonlinear P, PD, PI, and PID controllers are investigated using the Popov stability criterion. It is shown that for P and PD controllers, the nonlinear gain is unbounded for closed-loop stability. For PI and PID controllers, simple expressions are derived that relate the controller gains and system parameters to the maximum allowable nonlinear gain for stability. A numerical example is given for illustration. The stability of partially-nonlinear PID controllers is also discussed. Finally, the nonlinear PI controller is implemented as a force controller on a robotic arm and experimental results are presented. These results demonstrate the superior performance of the nonlinear PI controller relative to a fixed-gain PI controller. © 1998 John Wiley & Sons, Inc. 15: 161–181, 1998     

A local observability analysis method for a time-varying nonlinear system and its application in the continuous self-calibration system

Dear editor, Employing observability analysis of a dynamic system is necessary to determine the efficiency of a Kalman filter de-signed to estimate the state of...     

Design of optimal disturbance rejection PID controllers usinggenetic algorithms

This paper presents a method to design an optimal disturbance rejection PID controller. First, a condition for disturbance rejection of a control system-H_∞-norm-is described. Second, the design is formulated as a constrained optimization problem. It consists of minimizing a performance index, i.e., the integral of the time weighted squared error subject to the disturbance rejection constraint. A new method employing two genetic algorithms (GA) is developed for solving the constraint optimization problem. The method is tested by a design example of a PID controller for a servomotor system. Simulation results are presented to demonstrate the performance and validity of the method     

Backstepping design for time-varying nonlinear systems with unknown parameters

A simple backstepping design procedure is proposed and sufficient conditions for global partial state- and dynamic- feedback stabilization for a class of triangular systems with unknown time-varying parameters are derived.     

Robust design of stochastic controllers for nonlinear systems

The previous results are generalized on the stabilizing property of a control scheme designed for a class of discrete-time nonlinear stochastic systems. First, the existing controller is made more robust with a prescribed degree of stability by proper modifications. Next, the inherent robustness is illustrated by a design utilizing erroneous noise characteristics. Reconsideration of the stability analysis used allows one to treat a larger class of nonlinear stochastic systems with more general structures     

Globally robust nonlinear PID controllers for robot manipulators with an uncertain Jacobian matrix

Based on a continuous piecewise-differentiable increasing functions vector, a class of robust nonlinear PID (RN-PID) controllers is proposed for setpoint control with uncertain Jacobian matrix. Globally asymptotic stability is guaranteed and only position and joint velocity measurements are required. And stability problem arising from integral action and integrator windup, are consequently resolved. Furthemnore, RN-PID controllers can be of effective alternative for anti-integrator-wind-up,the control performance would not be very bad in the presence of rough parameter tuning.     

Suboptimal design of intentionally nonlinear controllers

A method of designing nonlinear controls for stationary plants is presented in the paper. The objective of the design is to produce soft-saturation-type constraints on certain state variables, such as velocity or acceleration. This is accomplished by formulating the problem as an optimization of a nonquadratic performance index. A sequence of suboptimal controls is then obtained. Although this sequence converges to the exact optimum solution, the procedure is stopped when the complexity of the resulting non-linear controller exceeds the design considerations of cost, size, and/or reliability. Experimental results of an actual design clearly indicate the desired velocity saturation effects.     

Integral criteria for optimal tuning of PI/PID controllers for integrating processes

Tuning formulas for PI/PID controllers for integrating processes are presented in this paper. The controller parameters are obtained by minimizing various integral performance index. Bacterial Foraging strategy, a new entrant to the family of evolutionary algorithms is used for minimization to avoid the local minima in the optimization procedure. A setpoint filter is used to reduce the large overshoot, and a significant improvement in control performance is obtained when compared to recently reported methods. Simulation results for an assumed perturbation in the plant delay are also given to illustrate the robustness of the proposed controller design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Combined design of structures and controllers for optimal maneuverability

This paper treats the problem of the combined design of structure/control systems for achieving optimal maneuverability. A maneuverability index which directly reflects the time required to perform a given maneuver or set of maneuvers is introduced. By designing the flexible appendages of a spacecraft, its maneuverability is optimized under the constraints of structural properties, and of the postmaneuver spill-over being within a specified bound. The spillover reduction is achieved by making use of an appropriate control design model. The distributed parameter design problem is approached using assumed shape functions and finite element analysis with dynamic reduction. Characteristics of the problem and problem solving procedures have been investigated. Adaptive approximate design methods have been developed to overcome computational difficulties. It is shown that the global optimal design may be obtained by tuning the natural frequencies of the spacecraft to satisfy specific constraints. We quantify the difference between a lower bound to the objective function associated with the original problem and the estimate obtained from the modified problem as the index for the adaptive refinement procedure. Numerical examples show that the results of the optimal design can provide substantial improvement.     

Wiener-Hopf design of optimal decoupling one-degree-of-freedom controllers

This reasonably self-contained paper is directed to the design of a multivariable optimal one-degree-of-freedom feedback loop which incorporates a decoupling controller in the forward path. The criterion for optimality is a quadratic-cost functional that penalizes both tracking error and saturation. The controllers on which optimization is based are general enough to allow for non-unity feedback and rectangular plant transfer matrices possessing normal row rank. Nevertheless, for the sake of brevity and clarity, attention is focused mainly on the square case. Earlier treatments of the problem have employed multi-degree-of-freedom controllers. The solution we present for the one-degree-of-freedom case is considerably more difficult to obtain, especially when saturation is taken into account. Explicit formulas are derived for the set of all decoupling controllers yielding finite cost, as well as those that are optimal. It is shown that these controllers are strictly-proper under conditions usually prevailing in practice. Four fully worked examples serve to illustrate many important numerical aspects of the theory and all major proofs are transferred to the Appendix.     

Uniformly optimal control of linear time-invariant plants: Nonlinear time-varying controllers

It is shown that in the problems of uniformly (or H^∞−) optimal control of linear time-invariant plants, arbitrary nonlinear, time-varying controllers offer no advantage over linear, time-invariant controllers.     

Controllability results for nonlinear impulsive integrodifferential evolution systems with time-varying delays

In this paper, we study the controllability results for the nonlinear impulsive integrodifferential evolution systems with time-varying delays in Banach spaces. The sufficient conditions of exact controllability is proved under without assuming the compactness of the evolution operator. The results are obtained by using the semigroup theory and the Schafer fixed point theorem.     

A probabilistic approach for designing nonlinear optimal robust tracking controllers for unmanned aerial vehicles

In this study, we propose a probabilistic approach for designing nonlinear optimal robust tracking controllers for unmanned aerial vehicles. The controller design is formulated in terms of a multi-objective optimization problem that is solved by using a bio-inspired optimization algorithm, offering high likelihood of finding an optimal or near-optimal global solution. The process of tuning the controller minimizes differences between system outputs and optimal specifications given in terms of rising time, overshoot and steady-state error, and the controller succeed in fitting the performance requirements even considering parametric uncertainties and the nonlinearities of the aircraft. The stability of the controller is proved for the nominal case and its robustness is carefully verified by means of Monte Carlo simulations.     

Graphical computation of gain and phase margin specifications-oriented robust PID controllers for uncertain systems with time-varying delay

This paper proposes a novel graphical method to compute all feasible gain and phase margin specifications-oriented robust PID controllers to stabilize uncertain control systems with time-varying delay. A virtual gain-phase margin tester compensator is incorporated to guarantee the concerned system with certain robust safety margins. The complex Kharitonov theorem is used to characterize the parametric uncertainties of the considered system and is exploited as a stability criterion for the Hurwitz property of a family of polynomials with complex coefficients varying within given intervals. The coefficients of the characteristic equation are overbounded and eight vertex Kharitonov polynomials are derived to perform stability analysis. The stability equation method and the parameter plane method are exploited to portray constant gain margin and phase margin boundaries. The feasible controllers stabilizing every one of the eight vertex polynomials are identified in the parameter plane by taking the overlapped region of the plotted boundaries. The overlapped region of the useful region of each vertex polynomial is the Kharitonov region, which represents all the feasible specifications-oriented robust PID controller gain sets. Variations of the Kharitonov region with respect to variations of the derivative gain are extensively studied. The way to select representative points from the Kharitonov region for designing robust controllers is suggested. Finally, three illustrative examples with computer simulations are provided to demonstrate the effectiveness and confirm the validity of the proposed methodology. Based on the pre-specified gain and phase margin specifications, a non-conservative Kharitonov region can be graphically identified directly in the parameter plane for designing robust PID controllers.     

Necessary conditions for the optimal control of a system with time-varying transport lags

Necessary conditions to be satisfied if the control of a system with time-varying transport lags is to be optimal, are derived. These correspond to the Euler-Lagrange equations, the first corner condition, and the transversality condition of the calculus of variations. The systems considered can be nonlinear, have a multivariable control, and contain a number of different transport lags. The states and controls of the system are assumed to be unbounded.     

A tuning strategy for multivariable PI and PID controllers using differential evolution combined with chaotic Zaslavskii map

A technique for tuning of decoupled proportional-integral (PI) and proportional-integral-derivative (PID) multivariable controllers based on a chaotic differential evolution (DE) approach is presented in this paper. Due to the simple concept, easy implementation and quick convergence, nowadays DE has gained much attention and wide application in solving continuous non-linear optimization problems. However, the performance of DE greatly depends on its control parameters and it often suffers from being trapped in local optimum. The application of chaotic sequences based on chaotic Zaslavskii map instead of random sequences in DE is a powerful strategy to diversify the population and improve the DE’s performance in preventing premature convergence to local optima. The optimized PD and PID controllers shows good closed-loop responses in control of the binary Wood–Berry distillation column, a multivariable process with strong interactions between input and output pairs. Some comparison results of PD and PID tuning using chaotic DE, classical DE and genetic algorithm are presented and discussed.     

一种PID参数量子粒子群自整定方法

传统的PID参数整定方法由于需要决策者具有较强的工程经验,难以处理非连续、非线性或时滞的复杂系统。针对这种情况,提出一种新的基于量子粒子群优化的PID参数自整定方法。该算法采用问题的时间绝对偏差乘积积分方程来评价粒子的适应值;设计一种时变变异算子,用来均衡粒子的全局和局部开发能力。实验结果表明,该算法在超调量和调节时间等指标上皆优于传统粒子群优化算法。