L.M. Hideg

Frequency domain analysis of learning systems

Frequency domain arguments on a general learning law are presented to verify claims of convergence which relax earlier requirements on the learning law transfer function. Known convergence properties are used to develop a pole-placement interpretation for an example for which simulations using a proportional-derivative learning law form are carried out. Physically relevant disturbances are introduced, and the ability of the learning law to damp out their effects is studied. A significant state-dependent disturbance is shown to be attenuated for reliable trajectory tracking.<<ETX>>

Time delays in iterative learning control schemes

Repeated accurate path tracking has many control applications. CNC machines in manufacturing or actuators in testing are examples. Repeated operations permits adjustments of control signals between cycles using trajectory error information. Learning control systems are well suited for this situation. Time delays in the plant or elsewhere can markedly affect control system stability even in repetitions. Calculation time by digital systems or by sampling techniques can cause delays. Sensor dynamics or sensor location can also cause delays. This paper proposes a stability condition for learning control where the plant exhibits a time delay.

Stability and convergence issues in iterative learning control. II

Repeated accurate path tracking has many control applications. Manufacturing or cycled endurance testing are examples. Repetitions permit adjustments of control signals between cycles with trajectory error information. Iterative learning control (ILC) systems are designed for this situation. Time delays can adversely affect stability especially in iterative schemes. Calculation time by digital systems or by sampling techniques can cause delays. Sensor dynamics or sensor location can also cause delays. This paper proposes a stability condition for ILC where the plant exhibits a time delay.

Equivalent Lyapunov and frequency domain stability conditions for iterative learning control systems

A system which repeatedly tracks a specified trajectory is considered. The error between a specified trajectory and the actual trajectory of system from the previous trial is used by an iterative learning control law in order to reduce this error on the current trial. Sufficient conditions which were developed by the authors for iterative learning system stability using Lyapunov stability theory are referenced. Necessary and sufficient conditions for iterative learning system stability using frequency domain analysis developed by the authors are also referenced. It is shown the these time and frequency domain stability conditions are equivalent.<<ETX>>

Stability of linear time varying multiple input multiple output continuous time learning control systems: a sufficient condition

Repeated accurate path tracking has many control applications. Manufacturing CNC machines or cycling actuators are examples. Effectiveness is limited to model accuracy, and complete information is not always available. Also, parameters may drift over time. Repeated operations permits control signal adjustments between cycles using trajectory error information. Learning systems are well suited for this situation. This paper proposes a sufficient condition for stability of linear time varying multiple input multiple output (MIMO) learning control systems.<<ETX>>

Coefficient test for discrete time learning system stability

A coefficient test for the stability of discrete time learning systems is developed. The test is based on the Jury criteria. Necessary and sufficient conditions result from the test. Several examples are provided.<<ETX>>

Design of a static neural element in an iterative learning control scheme

Most often, employing a neural net in a control system implies an adaption scheme. Neural nets inherently are non-model based, requiring the adaption. This paper proposes a design process which selects values of a single layer neural net suitable to replace a control law element.

Capstone term project for control systems curriculum

In teaching an undergraduate controls course, several concepts are introduced. Students often perceive these materials as unrelated, thus of little application. There is a need to unify these concepts into larger problems. Examples could be presented in class, however, this would create a passive roll for the student. To encompass a larger number of concepts and involve the students, the capstone term project was incorporated into the course. It requires a large amount of design effort, appropriate use of class concepts and the use of a simulation language. This satisfies ABET design requirements and adds to students credentials by requiring a simulator such as MATLAB to successfully complete the project. Sophistication of the project encourages collaboration and team effort among the students, serious design consultation with the instructor, and other elements of a working engineering environment. Project reports for credit are individual submissions.

A sufficient condition for the stability of linear time varying learning control systems: a robotic application

L. Hideg et al. (1990) described an equivalent time domain condition for learning control stability and compared it to the well known frequency domain condition (J. Craig, 1988). Here the authors expand the class of learning controls systems and plants whose stability can be studied with the time domain formulation. The stability condition considers a linear time-varying single-input system with dynamics inspired by a robot model. The fundamental learning control formulations are reviewed. The authors present the standard Lyapunov function, the difference Lyapunov, and, a reduction strategy on that difference Lyapunov and describe the sufficient conditions for stability. The application to a robot system is outlined, showing the sufficient conditions for stability found here are quite broad and robust.<<ETX>>

Velocity Profile Generation of a Robotic Manipulator to Minimize Tracking Error

The method described in this paper promotes accurate tracking of a given path by a robotic manipulator. The manipulators velocity along the path is slowed as manipulator singularities or path corners are encountered. This adjustment is necessary to keep the manipulator tracking close to the path to satisfy error criteria. A numerical example is presented.