Nader Sadegh

A perceptron network for functional identification and control of nonlinear systems

Tracking control of a general class of nonlinear systems using a perceptron neural network (PNN) is presented. The basic structure of the PNN and its training law are first derived. A novel discrete-time control strategy is introduced that employs the PNN for direct online estimation of the required feedforward control input. The developed controller can be applied to both discrete- and continuous-time plants. Unlike most of the existing direct adaptive or learning schemes, the nonlinear plant is not assumed to be feedback linearizable. The stability of the neural controller under ideal conditions and its robust stability to inexact modeling information are rigorously analyzed.

A Unified Approach to the Design of Adaptive and Repetitive Controllers for Robotic Manipulators

A unified approach, based on Lyapunov theory, for synthesis and stability analysis of adaptive and repetitive controllers for mechanical manipulators is presented. This approach utilizes the passivity properties of the manipulator dynamics to derive control laws which guarantee asymptotic trajectory following, without requiring exact knowledge of the manipulator dynamic parameters. The manipulator overall controller consists of a fixed PD action and an adaptive and/or repetitive action for feed-forward compensations. The nonlinear feedforward compensation is adjusted utilizing a linear combination of the tracking velocity and position errors. The repetitive compensator is recommended for tasks in which the desired trajectory is periodic. The repetitive control input is adjusted periodically without requiring knowledge of the explicit structure of the manipulator model. The adaptive compensator, on the other hand, may be used for more general trajectories. However, explicit information regarding the dynamic model structure is required in the parameter adaptation. For discrete time implementations, a hybrid version of the repetitive controller is derived and its global stability is proven. A simulation study is conducted to evaluate the performance of the repetitive controller, and its hybrid version. The hybrid repetitive controller is also implemented in the Berkeley</NSK SCARA type robot arm.

An exponentially stable adaptive control law for robot manipulators

This paper presents a new exponentially stable direct adaptive control law for motion control of robot manipulators. This control law utilizes the desired trajectory information instead of the actual manipulator joint signals for feed-forward compensations and paramater adaptation, and, computationally, it is extremely efficient. The exponential stability of the adaptive control algorithm is proven without requiring the persistent excitation condition and by fully considering the non-linear dynamics of the manipulator in the analysis.

State-Switched Absorber for Semi-Active Structural Control:

A system that has the capability to make instantaneous changes in its mass, stiffness, or damping may be termed a state-switchable dynamical system. Such a system will display different dynamical responses dependent upon its current state. For example, state-switchable stiffness may be practically obtained through the control of the termination impedance of piezoelectric stiffness elements. If such a switchable stiffness element is incorporated as part of the spring element of a vibration absorber, the change in stiffness causes a change in the resonance frequencies of the system, thereby instantaneously “retuning” the state-switched absorber to a new frequency. This paper briefly develops the fundamental analysis tools for a Single-Degree-of-Freedom state-switchable device, and then considers the application of such a device for the purpose of vibration control in a 2-DOF system. Simulation results indicate that state-switched vibration absorbers may be advantageous over classical passive tuned vibration absorbers under certain conditions.

Design and implementation of adaptive and repetitive controllers for mechanical manipulators

Synthesis and implementation results for a recently developed class of adaptive and repetitive controllers used for motion control of mechanical manipulators are presented. The repetitive controller, which learns the input torque corresponding to a repetitive desired trajectory, requires no explicit knowledge of the manipulator equations of motion. The adaptive controller, on the other hand, which estimates the robot dynamic parameters online, may be used for more general trajectories but requires more detailed modeling information. Both schemes are computationally efficient and require no acceleration feedback of any kind; only standard position and velocity feedback information is utilized. The performances of the above-mentioned controllers were experimentally evaluated on an IBM 7545 robotic manipulator and the results were compared to those of a simple PD (proportional-derivative) feedback system and a compound-torque controller. The repetitive algorithm outperformed the other controllers by a significant margin in terms of the tracking accuracy. >

A new repetitive controller for mechanical manipulators

A new repetitive learning controller for motion control of mechanical manipulators undergoing periodic tasks is developed. This controller does not require exact knowledge of the manipulator dynamic structure or its parameters, and is computationally efficient. In addition, no actual joint accelerations or any matrix inversions are needed in the control law. The global asymptotic stability of the ideal and the robust stability of the nonideal control system is proven, taking into account the full nonlinear dynamics of the manipulator. Simulation results of this algorithm applied to a realistic Scara type manipulator, which includes dry friction, pay-load inertia variations, actuator/sensor noise, and unmodelled dynamics are also presented.

Minimal realization of nonlinear systems described by input-output difference equations

We consider a general class of nonlinear discrete-time systems described by their input-output (I/O) relationship. We first present the necessary and sufficient conditions for existence of a local observable state-space realization of the system and an explicit algorithm for computing it. In cases where the I/O map and its resulting realization are nonminimal, we formulate an algorithm for extracting its minimal realization whenever possible. The developed theory and algorithms are illustrated by means of several examples.

Theory and Implementation of a Repetitive Robot Controller With Cartesian Trajectory Description

This paper presents a new repetitive learning controller for motion control of mechanical manipulators undergoing periodic tasks defined in Cartesian space. The controller does not require knowledge of the manipulator dynamic parameters beyond a simple geometric description. The desired task will be defined in Cartesian coordinates, and no inverse kinematics or inverse Jacobian will be calculated. The asymptotic stability of this algorithm is proven using the Lyapunov approach, and the nonlinear characteristics of the manipulator are explicitly taken into account. The results of implementation of this new repetitive learning controller on an IBM 7545 robotic manipulator are presented. Cartesian feedback was obtained from optical joint position encoders using forward kinematics, and velocity was estimated by simple numerical differentiation of the Cartesian position signal in software. The performance of the algorithm was compared to that of a simple PD feedback system, and a modified “Computed Torque” controller using inverse kinematics on the Cartesian path. The learning algorithm outperformed both of these controllers by a significant margin, exhibited convergence within approximately three cycles, and did not require inverse kinematics to execute the Cartesian path.

Modelling an Electro-Hydraulic Poppet Valve

Abstract This paper develops the dynamic modelling of a novel two-stage bidirectional poppet valve and proposes a simplified model that is more suitable for control purposes. The dynamic nonlinear mathematical model of this Electro-Hydraulic Poppet Valve (EHPV) is based on the analysis of the interactions among its three internal systems: the mechanical, hydraulic, and electromagnetic system. A discussion on the employed experimental methodology is included along with the validation of this model. When the pressure differential across the valve is sufficiently high and does not vary considerably, the model for this valve can be simplified substantially. More specifically, the EHPV can be modelled as a linear second order system with a static input nonlinearity. This nonlinearity is realized from the valves steady state characteristics. The advantage of this separation between valve dynamics and nonlinearities is that an inverse linearisation approach (to cancel the nonlinearity) can be used to facilitate the control task for the valve.

Minimum Time Trajectory Optimization and Learning

This paper presents a numerical algorithm for finding the bang-bang control input associated with the time optimal solution of a class of nonlinear dynamic systems. The proposed algorithm directly searches for the optimal switching instants based on a projected gradient optimization method. It is shown that this algorithm can be made into a learning algorithm by using on-line measurements of the state trajectory. The learning is shown to have the potential for significant robustness to mismatch between the model and the system. It learns a nearly optimal input through repeated trials in which it utilizes the measured terminal state error of the actual system and gradients based on the theoretical state equation of the system but evaluated along the actual state trajectory. The success of the method is demonstrated on an under-actuated double pendulum system called the acrobot.