Specific Control Law Research Articles

Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms

Adaptive robust control (ARC) of MIMO nonlinear systems transformable to two semi-strict feedback forms are considered. The forms can have both parametric uncertainties and uncertain nonlinearities such as external disturbances. In addition, the forms allow coupling and appearance of parametric uncertainties in the input matrix of each layer. Furthermore, the usual assumption on the linear parametrization of the state equations is relaxed to the extent that the forms are applicable to the control of some mechanical systems. To deal with the complexity and difficulties caused by the coupling and the appearance of parametric uncertainties in the input matrices, an ARC Lyapunov function—an extension of the adaptive control Lyapunov function (aclf )—is used to formalize the viewpoint and the achievable results of the recently proposed ARC approach. Two backstepping designs via ARC Lyapunov functions are presented. The results are then used to construct specific ARC control laws for MIMO nonlinear systems in the semi-strict-feedback forms. By using trajectory initialization, the resulting ARC law achieves a guaranteed output tracking transient performance and final tracking accuracy in general, while keeping all physical states and control inputs bounded. In addition, the control law achieves asymptotic output tracking in the presence of parametric uncertainties without using a discontinuous or infinite-gain feedback term.

Deployable Truss Operation by ETS‐VII Robot Arm Using Force Accommodation Control

An experiment for teleoperating a truss structure has been performed as part of a space robotics mission on Engineering Test Satellite No. 7 (ETS‐VII). This article reports the results from truss experiments conducted by means of the ETS‐VII robot arm using force accommodation control, which is a specific control law developed for the ETS‐VII robot arm. With this control function, the robot arm moves toward the point where the external force becomes the command value, which is sent from the ground. This control technique is useful especially in the case of teleoperation with time delay, since excessive force and torque can be avoided, and in addition, no a priori trajectory information is required. However, the robot arm cannot attain the desired configuration for itself. These characteristics can be used for deployable and assembly truss operation, making full use of merits and avoiding demerits. The effectiveness is confirmed through an ETS‐VII onboard experiment.

Bounds on achievable performance in the identification and adaptive control of time-varying systems

Treats the identification and adaptive control of time-varying linear systems. For linear systems with a Gauss-Markov parameter process a global lower bound on the mean square error is obtained which is valid for any causal parameter estimator. A similar lower bound is obtained for any causal, one step-ahead predictor. These bounds are applied to the adaptive control of time-varying systems to obtain a lower bound on closed-loop mean square performance for any causal control law. For a specific control law, mean square stability is established, and through simulations it is seen that the performance nearly meets the theoretical lower bound.

Stabilization of a Class of Nonlinear Systems by a Specific Nonlinear Observer

Based on the idea of special purpose observers, a new approach to the observer-based stabilization of a class of nonlinear systems by means of I/O linearization is proposed. The class of the system is assumed to be I/O linearizable and Complete Uniformly Local Weakly Observable with an Input-to-State Stable internal dynamics.The strategy considered in this paper is as follows. At first the system of interest is cascaded with a chain of integrators to extend its relative degree to system order, and then observer-based I/O linearization control law is designed to yield stability for the enlarged closed loop system.It is shown that for implementing such a specific control law the linear structured observer is valid.

Simulation Models for French Praxitele Project

The Praxitele project was charged with designing a new kind of transportation in an urban environment, which consisted of a fleet of electric public cars. These public cars are capable of autonomous motion on certain displacements between stations. The realization of such a project requires experimentation regarding the behaviors of autonomous vehicles in the urban environment. Because of the danger connected with these kinds of experiments at a real site, it was necessary to design a virtual urban environment in which simulations could be done. To perform an authentic simulation of a real environment composed of a large set of vehicles (some of which are autonomous and others of which are controlled by the user or by some specific control law), different models need to be implemented: geometric modeling of the environment, mechanical simulation, motion control models, driver models, sensor models, and visualization algorithms. To implement these different models into a unique system, a new simulator system was designed. This simulator takes into account real-time synchronization and communication between cooperative processes implementing the models mentioned earlier. First, the aims and goals of the Praxitele project are presented. The motion control algorithm for automatic platooning of autonomous vehicles is then briefly presented. The focus is on the simulation of a virtual urban environment that includes Praxitele vehicles. The implementation of all of these models is described. Finally, results of a simulation of cooperative driving of the Praxitele vehicles in a virtual urban environment are given.

Simulation Models for French Praxitele Project

The Praxitele project was charged with designing a new kind of transportation in an urban environment, which consisted of a fleet of electric public cars. These public cars are capable of autonomous motion on certain displacements between stations. The realization of such a project requires experimentation regarding the behaviors of autonomous vehicles in the urban environment. Because of the danger connected with these kinds of experiments at a real site, it was necessary to design a virtual urban environment in which simulations could be done. To perform an authentic simulation of a real environment composed of a large set of vehicles (some of which are autonomous and others of which are controlled by the user or by some specific control law), different models need to be implemented: geometric modeling of the environment, mechanical simulation, motion control models, driver models, sensor models, and visualization algorithms. To implement these different models into a unique system, a new simulator system was designed. This simulator takes into account real-time synchronization and communication between cooperative processes implementing the models mentioned earlier. First, the aims and goals of the Praxitele project are presented. The motion control algorithm for automatic platooning of autonomous vehicles is then briefly presented. The focus is on the simulation of a virtual urban environment that includes Praxitele vehicles. The implementation of all of these models is described. Finally, results of a simulation of cooperative driving of the Praxitele vehicles in a virtual urban environment are given.

Safe and time-optimized power transfer between two induction loads supplied by a single generator

The paper deals with the problem of transferring power between different induction loads supplied by the same current generator, in as short a time as possible. In the reference solution, the system is completely stopped: it needs a long time for the current to reach zero and, afterwards, its new value, because the DC link inductance must be demagnetized and remagnetized; moreover an auxiliary starter is needed. In the proposed solution, the input of the current inverter is short-circuited whenever a transfer must be performed; the inductance remains magnetized and the current at the output of the inverter varies very quickly. The transfer time is minimal, and no starter is needed; the specific inverter control laws used to insure natural commutation are described. The paper also, presents control models of the system, obtained by using the first harmonic modeling method. >

Linear Feedback Control of Position and Contact Force for a Nonlinear Constrained Mechanism

A feedback control problem for a constrained mechanism is formulated and solved. The mechanism is controlled by forces applied to the mechanism which are to be adjusted according to a linear control law, based on feedback of the positions and velocities of the mechanism and feedback of the constraint force on the mechanism. The control objective is to achieve accurate and robust local regulation of the motion of the mechanism and of the constraint force on the mechanism. Derivation of a suitable control law is significantly complicated by the nonclassical nature of the differential-algebraic model of the constrained system and by the nonlinear characteristics of the model. The control design approach involves use of a certain nonlinear transformation which leads to a set of decoupled differential-algebraic equations; classical control design methodology can be applied to these latter equations. An example of a planar mechanism is studied in some detail, for two different regulation objectives. Specific control laws are developed using the described methodology. Comparisons are made with a closed loop system, where the control law is derived without proper consideration of the constraint force. Computer simulations are presented to demonstrate the several closed-loop properties.

Sensor and actuator selection for large space structure control

This paper presents an algorithm that aids the controls engineer in specifying a sensor and actuator configuration for regulation of large-scale, linear, stochastic systems such as a large space structure model. The algorithm uses a linear quadratic Gaussian controller, an efficient weight-selection technique based on successive approximation, and a measure of sensor and actuator effectiveness to specify a final sensor and actuator configuration. This configuration enables the closed-loop system to meet output specifications with minimal input power. The algorithm involves no complex gradient calculations and is numerically tractable for large linear models, as demonstrated by the solar optical telescope example in this paper. Additionally, the algorithm provides the controls engineer with information on the important design issues of actuator sizing, reliability, redundancy, and optimal number. HE advent of the Space Shuttle makes the large space structure (LSS) an imminent reality. These future space structures will be measured in kilometers and, of necessity, will be lightweight and highly flexible (light damping). Standard LSS missions will include power generation, surveillance, astronomy, and communications. These missions will require stringent pointing accuracy, shape control, and vibration suppression. To satisfy these demanding mission requirements, the LSS will almost certainly require an active, regulator-type controller with multiple sensors and actuators located throughout the structure.i-6 Furthermore, given the size of an LSS, there will be a large set of admissible sensor and actuator locations. The controls engineer then faces the problem of selecting a limited number of sensor and actuator locations to best the LSS mission. The term best in this paper means achieving the LSS output specifications with minimal actuator power. The solution to this sensor and actuator selection (SAS) problem needs at least the following ingredients: 1) A specific closed-loop control law structure; 2) a technique for systematically adjusting (tuning) control law parameters to achieve output specifications with minimal power; and 3) a technique to evaluate the effectiveness of possible sensor and actuator configurations in achieving output specifications with minimal power. This paper incorporates the preceding ingredients into an algorithm that solves the SAS problem for an LSS modeled as a linear stochastic system. Some necessary background information on linear stochastic systems and linear quadratic Gaussian (LQG) control theory are presented in Sec. II along with a formal statement of the SAS problem. Section III contains two important selection theorems, four pertinent facts, and the general flow of the SAS algorithm. Results from the SAS algorithm applied to the controller design for a large space telescope are presented in Sec. IV, and Sec. V contains concluding remarks.

Feedback control for non-linear singular systems

An invertible non-linear map is developed, which transforms a non-linear singular system into a regular one and preserves local properties under the application of specific feedback control laws. The presented algorithm is easily implementable on a digital computer, since it is of closed form. An application of the above algorithm is presented on an autonomous vehicle.

An optimal feedback control for a bilinear model of induction motor drives†

Abstract The use of optimization techniques for the control of drives using a frequency controlled induction motor as an actuator is considered. The approach proposed is based on the choice of a specific control law in the framework of a prefixed class of stabilizing feedback controls. The optimized performance index is obtained a posteriori by applying the Bellmann's principle to a problem with an index in which the term depending on the state is initially unspecified. Successively, the control law is developed, and it is proved how it minimizes a particular index which takes into account both the influence of the error and the control effort. This index has proved very useful in the control choice since it makes it possible to determine a correspondence between the elements of the weighting matrices and the system transient behaviour.

Sensitivity Considerations in Specific Optimum Controls

ABSTRACT This paper considers the problem of sensitivity of the specific optimum control law to changes in the initial conditions and duration of optimization of a linear dynamic system. Examples are included to illustrate the method.

Stabilization of a Satellite via Specific Optimum Control

The Optimum Stabilization of a tumbling satellite via Hamilton-Jacobi theory has been reported by one of the authors before in ?On the optimum stabilization of a satellite? [2]. This companion paper discusses the synthesis of a specific optimum control law for the same problem and compares the results with the optimum solution. It is shown that a specific optimum control law yields, acceptable performance while being much easier to instrument than the optimum control law.