A. Balestrino

Paper: Nonlinear adaptive model-following control

The use of discontinuous control in adaptive model-following continuous control systems with nonlinear time-varying plant is described. The first approach is based on the theory of variable structure systems. Hyperstability theory is the basis of the second scheme; the third one results by combining the previous approaches. The link among the three approaches is explored by studying the error dynamics. Practical implementation and applications are discussed.

Robust Control of Robotic Manipulators

Abstract Typically the dynamic control of robotic manipulators is characterized by two levels. The first one requires coordinate transformations to convert the desired path from Cartesian to joint space. The second one requires the computation of generalized torque inputs starting from the knowledge of the manipulator dynamic model. The problems at both levels are difficult to solve because of the high nonlinearities, parametric variations and inaccuracies which occur. Using adaptation control laws, valid for nonlinear time-varying plants, a robust control technique is developed at the second level forcing the controlled manipulator to follow the behaviour of a decoupled linear time invariant system. The problem of converting coordinates is reformulated as a nonlinear dynamic problem and is solved again by making use of robust adaptive techniques. The amount of computation is limited and the precision obtainable is very satisfactory as shown by simulation results.

Hyperstable adaptive model following control of nonlinear plants

Based on hyperstability theory, a new adaptation law for adaptive model-reference control systems is developed, for use with a class of nonlinear time-varying plants. Assuming some structural conditions to be verified, a simple and systematicdesign procedure is suggested whose one prerequisite is a knowledge of the range of variation of the plant parameters. The adaptation mechanism involves no on-line integration of differential equations and it is easily implemented by means of microprocessors. The dynamic behaviour is clarified by treating the adapted system as a variable structure system.

A generalised approach to the stability analysis of PWM feedback control systems

Abstract A unified approach to stability analysis of feedback control systems with pulse-width modulators is discussed. The proposed procedure is developed on the basis of the discrete analog of Lyapunovs method, with no limiting hypothesis on the structure of the controlled plant and of the modulation law. The analysis is exemplified particularly for lead-type PWM control systems. Significant plant classes are investigated, and the critical values of parameters in a closed form are determined which assure asymptotic stability of the steady-state solution, whatever the reference input may be.

An algorithmic approach to coordinate transformation for robotic manipulators

Coordinate transformation is one of the most important issues in robotic manipulator control. Robot tasks are naturally specified in work space coordinates, usually a Cartesian frame, while control actions are developed on joint coordinates. Effective inverse kinematic solutions are analytical in nature; they exist only for special manipulator geometries and geometric intuition is usually required. Computational inverse kinematic algorithms have recently been proposed; they are based on general closed-loop schemes which perform the mapping of the desired Cartesian trajectory into the corresponding joint trajectory. The aim of this paper is to propose an effective computational scheme to the inverse kinematic problem for manipulators with spherical wrists. First an insight into the formulation of kinematics is given in order to detail the general scheme for this specific class of manipulators. Algorithm convergence is then ensured by means of the Lyapunov direct method. The resulting algorithm is based on ...

Adaptive Control Design in Servosystems

Abstract The increased demand on electrical drives performances leads to the use of advanced control structures. An adaptive model following control system for d. c. drive is developed via hyperstability theory. A new control algorithm is proposed that produces a discontinuous control signal, similar to a bang-bang control, so that particular trajectories, referred as sliding modes, occur. The design procedure is simple and effective and leads to a controller that can be implemented by means of signum function and ordinary linear functions. The tracking characteristics, along with the insensitivity to parametric variations, are evidenced by means of experimental tests.

On the Ordinary and Modified Subharmonic Control

Abstract In this paper multiple pulse width modulation processes in power converters are analysed. The modulator output spectrum is given in terms of the single harmonic components. The computation heavily relies on the theory of Kapteyn series by which the implicit equations concerning the switching instants are explicitely solved. The method of subharmonic control is thoroughly examined and subharmonics occurrence is stressed. Besides, a modified technique is pointed out, with a spectrum characterized only by odd harmonics of the modulating frequency. A comparison among different modulation techniques is worked out.

Hyperstable Variable Structure Control for a Class of Uncertain Systems

Abstract A new approach to control for a class of uncertain systems is set forth combining hyperstable adaptive model following control and variable structure system control. The procedure retains the advantages of both approaches so that the designer can specify the dynamics during the sliding motion and the rate of convergence to the sIiding hyperplane. An application of the proposed approach to the control of robotic manipulators shows the robustness and the feasibility of such procedure.

On the stability of thyristor phase-controlled converters

SUMMARY This paper is concerned with the stability of thyristor-bridge control systems and develops the theoretical basis for the bridge model and its implications. By considering the solution of the differential, equation governing the current delivered to a series R-L load, an exact nonlinear difference equation is established. The behaviour of the system, both statically and dynamically, is related to the controller and converter structure, to the reference input and to the firing pulses control law. Both the one-quadrant and two-quadrants converters are examined with a proportional integral controller. The analysis techniques are proper of the non-linear sampled data systems.

On the analysis of chopper drives with pulse width modulators

SUMMARY Chopper amplifiers, converters and other similar devices may be modelled as pulse width modulators with natural sampling. Feedback control systems which use natural sampling modulators as power amplifiers are generally muchmore difficult to treat mathematically than uniform sampling ones. In order to overcome these difficulties some equivalent models are set forth in the form of nonlinear uniformly sampled data systems. Lead and lag type pulse width modulators are extensively investigated. As far as critical gains are concerned, the proposed models are evaluated by determining the stability boundaries. The procedure is exemplified by taking into account a critical second order controlled plant.