Synthesis Of Control Law Research Articles

Stabilization of Optimum Trajectory Costate Differential Equations

Introduction I N trajectory optimizationand synthesis of initial-valueand twopoint boundary-valueguidance and control laws, most applications of the Euler–Lagrange Ž rst-variation necessary conditions of the calculusof variationshave led to asymptoticallyunstablecostate differentialequationsand, hence,unstablebehaviorof systemphysical states.This instabilityhas beenmost troublesomewhen solving for long-durationextremal arcs, particularlywhen signiŽ cant statedependent nonlinear forces act on the  ight vehicle. For example, the purposemight be to designminimum fuel consumptiontrajectories for cruising  ight of a high L=D aircraft; the optimumsolutions may involve sustainedphugoidal oscillations, but that behavior can be obscured by rapid costate divergence. ThisEngineeringNote introducesamethod for stabilizingcostate differential equations via analytical phase adjustment of the timevarying costates. The method employs a time-varying phaseadjustment parameter. For a given model of the vehicle dynamics, a necessary lower bound on the phase-adjustment parameter is derived, and a stronger sufŽ cient condition is suggested. For simplicity, the subject is here presented in the context of a Ž rst-order one-dimensionalsystem,but extensiontomultidimensionalsystems is straightforward. Consider Ž rst a one-dimensionalguided object (such as a sled or railcar) that moves horizontallyon a straight path and has the linear, time-invariant state equations:

Aeroacoustoelasticity in state-space format using CHIEF regularization

This paper deals with aeroacoustoelastic modeling for analysis of the acoustic field inside an aircraft cabin. The aim is the identification of a state-space format for aeroacoustoelasticity equations applicable, for instance, for synthesis of an active control law devoted to cabin noise abatement. Specifically, attention is focused on the development of the aeroelastic operator, starting from a boundary integral equation method for the exterior compressible-aerodynamics solution. As is well known, in such a type of application of the boundary integral equation method, singularities occur in the algebraic equations resulting from discretization of the integral operator. Here, the discretized aerodynamic operator is regularized by using the CHIEF technique, that consists of augmenting the algebraic problem with homogeneous conditions at points in the interior domain (the cabin space, in our problem). Then, in order to obtain the state-space format model of the aeroacoustoelastic operator, the resulting trascendental aerodynamic transfer functions between structural Lagrangean variables and generalized aerodynamic forces are approximated through rational polynomials, and the additional aerodynamic states induced by their poles are included in the set of state-space variables.

Optimal fault detection in a closed-loop framework: a joint approach

The work reported in this paper focuses on an optimal joint synthesis of control law and fault detection algorithm in the presence of model uncertainties. The method developed takes the interactions between control and diagnosis into account. A quadratic criterion combining both control and diagnosis aims is developed in a worst case situation according to model uncertainties and disturbances. The residual evaluation is carried out using a threshold based on an uncertain closed-loop framework. Finally, the joint synthesis is illustrated and compared to a sequential design of the algorithms through the application to an hydraulic process.

Three-axis Attitude Control for Flexible Spacecraft by Lyapunov Approach under Gravity Potential

Attitude control law synthesis for the three-axis attitude maneuver of a flexible spacecraft model is presented in this study. The basic idea is motivated by previous works for the extension into a more general case. The new case includes gravitational gradient torque which has significant effect on a wide range of low earth orbit missions. As the first step, the fully nonlinear dynamic equations of motion are derived including gravitational gradient. The control law design based upon the Lyapunov approach is attempted. The Lyapunov function consists of a weighted combination of system kinetic and potential energy. Then, a set of stabilizing control law is derived from the basic Lyapunov stability theory. The new control law is therefore in a general form partially validating the previous work in some sense.

A new robotic drive joint friction compensation mechanism using neural networks

The knowledge of realistic dynamic models to robotic actuators would be of great aid in the synthesis of control laws to robot manipulators, mainly in cases of great precision robotic or even for manipulators with flexible links. In this paper we present a training scheme and propose a structure of neural network (NN) to learn the friction torque of a geared motor drive joint robotic actuator. To train the NN was used experimental data obtained by an harmonic-drive actuator, equipped with an encoder to measure the rotor angular position. It was considered the motor torque and the rotor angular velocity as NN input, while the friction torque was the only output, which was used in the proposition of a non-linear friction compensation mechanism. The experimental results attested the efficiency of the NN friction estimation and compensation with the proposed mechanism.

Performance tuning of robust motion controllers for high-accuracy positioning systems

This paper presents a structural design method of robust motion controllers for high-accuracy positioning systems, which makes it possible to tune the performance of the whole closed-loop system systematically. First, a stabilizing control input is designed based on Lyapunov redesign for the system in the presence of uncertainty and disturbance. And adopting the internal model following control, robust internal-loop compensator (RIC) is proposed. By using the structural characteristics of the RIC, disturbance attenuation properties and the performance of the closed-loop system determined by the variation of controller gains are analyzed. Next, in order to design a robust motion controller for a high performance positioning system, dual RIC structure is proposed and it is shown that if the synthesis of the robust motion control law is performed in the RIC framework, the robust property of RIC can be naturally implanted in the feedback controller. The proposed structural design of robust motion controller provides a systematic approach to the problem of robust stability and performance requirement in the face of uncertainty. Furthermore, by allowing the tradeoffs between robust stability and performance to be quantified in a simple fashion, it can illuminate systematic design procedure of the robust motion controllers. Finally, the proposed method is verified through simulation and the performance is evaluated by experiments using a high-accuracy positioning system.

A proposal of handling qualities shaping for general aviation aircraft

A proposal of the perspective solution of the general aviation aircraft control system is presented. The objective of the proposed concept for the control system is to assist pilots with limited aviation training by: automatic stabilization of the aircraft's attitude, altitude, airspeed, and heading and decoupling of the flight controls. The structure and main functions of the control system is presented, and method of control laws synthesis is proposed. Flight control system is based on the model‐following design technique. Two kinds of flight control systems are taken into consideration. The first solution is based on the optimal full‐state feedback controller, the second one is the simplified controller, using the easy observed states for feedback loop only. The project calculation of the flight control system for PZL‐110 “Koliber” aircraft, computer simulations and preliminary flight testing results will be presented.

Sliding-mode control scheme for a class of continuous chemical reactors

The synthesis of a robust control law for regulation control of a class of relative-degree-one nonlinear systems is presented. The control design is based on a sliding-mode uncertainty estimator, developed under a framework of algebraic-differential concepts. The closed-loop stability for the underlying closed-loop system is achieved via averaging techniques. Robustness of the proposed control scheme is proved in the face of noise measurements, model uncertainties and sustained disturbances. The performance of the proposed control law is illustrated with numerical simulations, comparing the proposed controller with a well tuned PI controller.

Advanced control and stability of autonomous road vehicles. Part II: Practical stability of road vehicles

The paper describes for the first time the conditions for practical stability of the road vehicle as a complex system in interaction with the dynamic environment. Stability analysis is based on knowledge of the road vehicle model dynamics as well as the dynamic environment model, developed specially for that purpose and for the synthesis of the dynamic control laws applied in the system automatic control. The stability conditions for two dynamic control laws, the pure position control and the combined position/force control low, were derived. In the chosen example, the procedure for determining control parameters was described using the vehicle practical stability test. In addition, characteristic simulation results, obtained by applying the proposed dynamic position/force control law, were presented for the case of a stable closed-loop system with variable system parameters. Finally, fundamental characteristics of the novel approach are pointed out and possible research directions outlined.

DECENTRALIZED HIERARCHICAL STOCHASTIC CONTROL IN A LARGE SCALE STATIC SYSTEM

In the paper a synthesis of control law for a large scale stochastic system is presented. The large scale system composed of M linear static subsystems with an-iteraction and quadratic performance index are considered. A two-level hierarchical control structure is assumed, in which a coordinator and local controllers have access to different information. A suboptimal algorithm, in which it is possible to partially decompose calculations and to realize decentralized control, is proposed. A simple example is presented.

Control law design for haptic interfaces to virtual reality

The goal of control law design for haptic displays is to provide a safe and stable user interface while maximizing the operator's sense of kinesthetic immersion in a virtual environment. This paper outlines a control design approach which stabilizes a haptic interface when coupled to a broad class of human operators and virtual environments. Two-port absolute stability criteria are used to develop explicit control law design bounds for two different haptic display implementations: the impedance display and admittance display. The strengths and weaknesses of each approach are illustrated through numerical and experimental results for a three degree-of-freedom device. The example highlights the ability of the proposed design procedure to handle some of the more difficult problems in control law synthesis for haptics, including structural flexibility and noncollocation of sensors and actuators.

Fuzzy speed and steering control of an AGV

The development of techniques for lateral and longitudinal control of vehicles has become an important and active research topic in the face of emerging markets for advanced autonomous guided vehicles (AGVs) and mobile robots. In this respect, there has been much literature published, although not so much on the actual performance of such controllers in a practical setting. The primary focus in this paper is on the development and actual implementation of intelligent and stable fuzzy proportional derivative-proportional integral (PD-PI) controllers for steering and speed control of an AGV. The AGV used in this study is an electrically powered golf car, suitably modified for autonomous navigation and control. The use of fuzzy logic for control law synthesis, among other things, facilitates the incorporation of control heuristics, while guaranteeing stability, uncoupling steering control from speed control and providing for easy incorporation of a braking controller. Through experimentation, the designed controllers are demonstrated to be insensitive to parametric uncertainty, load and parameter fluctuations and, most importantly, amenable to real-time implementation. The performance of the proposed uncoupled direct fuzzy PD/PI control schemes for this particular outdoor AGV is also compared against conventional proportional-integral-derivative (PID) controllers. Experimental results demonstrate that the proposed fuzzy logic controllers, which are synthesized from a variable structure systems viewpoint, also outperform conventional PID schemes, particularly in tracking accuracy, steady-state error, control chatter and robustness.

A system approach for control development of lower-limbs training machines

This paper presents the approach undertaken for the specification and design of the control system of a machine for training and rehabilitation of lower limbs. The resulting hybrid and hierarchical control system interprets the training specifications provided by a physiotherapist for a particular user to execute the corresponding sequence of switching (position, velocity and force) control laws. A generic model, based on the use of an object extension of Statecharts, is proposed for the sequential part of the controller. The design and synthesis of the switching control laws are illustrated for the case of the machine Multi-Iso. Some illustrative training results are also discussed.

Modeling of an acousto-optic laser beam steering system intended for satellite communication

High data rate of laser communication systems should be matched by wide operational bandwidth of beam positioning. This could be achieved by the application of nonmechanical beam steering technologies utilizing acousto-optic phenomena. Major components of acousto-optic beam steering systems, a Bragg cell, and a quadrant detector are subjected to comprehensive laboratory testing and characterization as components of a control system. A mathematical and computer simulation model of the entire steering system addressing system dynamics, cross coupling of azimuth and elevation channels, and nonlinearity, and facilitating synthesis of advanced control laws is developed.

Synthesis of Control Law for Non-Linear Systems in Critical Case

Stabilization (control system design) is one of fundamental areas investigated in the system theory and many articles have already been dedicated to it in technical literature. The paper deals with a stabilization method for a certain class of non-linear systems. Non-linear systems belonged to the considered class have (after performed approximative linearization) some poles on the imagine axis which are uncontrollable. As the theoretical base of the approach presented in the paper the Center manifold theory (which enables us to solve the stabilization problem) has been chosen.

Controller Design for High-Performance Thrbomachines

This paper describes the development of an optimal control law design for the lateral vibration sup pression and stabilization of a rotor system with anisotropic fluid-film bearings and fluid leakage. Evaluation of the degree of controllability and observability and synthesis of the optimal control law using linear quadratic regulator theory accompanied by an asymptotic state observer are performed. Time responses, steady-state behavior, and singular value analysis are used to evaluate the performance and robustness of the feedback control system. Good closed-loop characteristics are obtained.

Control Laws synthesis of multi-arm cooperating robots with elastic interconnection at the contacts

The problem of the control of the object cooperative manipulation during the work of multiple non-redundant six degrees-of-freedom manipulators is considered in this paper. The problem of the cooperative manipulation control is, like all its problems, solvable only if the system is considered as the elastic one, taking into account all existing constraints. The controlled system is with the output number greater than the available number of inputs, therefore, in the first stage the desired motions are selected from the set of the possible nominal ones, containing the trajectories of the manipulated object mass centre and slave manipulators contacts. Afterward, the classification of control tasks is performed. The procedure for the calculation of the driving torques introduced into the joints of the manipulators, necessary to obtain the nominal trajectory tracking, is proposed. The theoretical analysis of cooperative system closed loop behaviour is exposed, particular attention being paid to the uncontrolled variables. The procedure is illustrated on the example of the simple closed loop cooperative system, consisting of the manipulated object and two one degree-of-freedom manipulators. For this system, the behaviour is determined and the driving torques are calculated.

Robust state-predictive control with separation property: A reduced-state design for control systems with non-equal time delays

A robust state-predictive control strategy is proposed for discrete-time multi-input/output systems with non-equal delays on signal buses. It is based on a separation property between control and prediction. The input delays are taken into account in the control law synthesis and the output delays are handled using an original steady-state Kalman predictor of order equal to the length of the state of the system without delays. Robustness, especially against uncertain delays, is improved using a state extension in the predictive gain synthesis. The classic optimal separation theorem (in the case of an one step predictor) is extended to the general case of a d+1 step prediction for a delayed discrete-time system.

Artificial Intelligence Based Synthesis of Semiactive Suspension Systems

This paper is concerned with the synthesis of control laws for semiactive suspension systems employing artificial intelligence. A review is made of a simple, 2-degree-of-freedom, quarter car model with passive, active, and semiactive control. An active linear quadratic Gaussian controller and a semiactive, balance logic derived controller are then used to develop two artificial intelligence based controllers-a semiactive neurocontroller and a semiactive fuzzy logic controller. This paper focuses on the advancement of balance semiactive logic using variable dry friction and the development of fuzzy semiactive controllers. The concerns in view are twofold: the reduction in cost of the control system and the antichattering nature of the logic. The development is from an engineering perspective and attempts to reduce the well-known schism between theoreticians and users of feedback control.

On the boundedness of the Hessian of the potential energy of robot manipulators

Several results on robot manipulator motion control require a uniform bound for the Hessian of the potential energy or equivalently the Jacobian of the gravity vector. Not all robot manipulators, however, ensure the existence of such a uniform bound. The first contribution of this article is the complete characterization of this class which is referred to as class ℬ manipulators. The uniform bound of the Hessian is typically part of the control law expression and hence it plays an important role in controller gain synthesis. The second contribution of this article consists of deriving, for class ℬ robot manipulators, an easy to compute explicit expression of the uniform bound in terms of kinematic and inertial link parameters. If for a particular robot manipulator the Hessian of potential energy is not uniformly bounded, a bound exists that is valid within the physical workspace of the manipulator. The third contribution of this article is the derivation of an explicit expression for the latter bound which is useful in the design and controller gain synthesis of control laws that are valid locally. ©1999 John Wiley & Sons, Inc.