P. Lohnberg

A supervisor for control of mode-switch processes

Many processes operate only around a limited number of operation points. In order to have adequate control around each operation point, and adaptive controller could be used. When the operation point changes often, a large number of parameters would have to be adapted over and over again. This makes application of conventional adaptive control unattractive, which is more suited for processes with slowly changing parameters. Furthermore, continuous adaptation is not always needed or desired. An extension of adaptive control is presented, in which for each operation point the process behaviour can be stored in a memory, retrieved from it and evaluated. These functions are co-ordinated by a ?supervisor?. This concept is referred to as a supervisor for control of mode-switch processes. It leads to an adaptive control structure which quickly adjusts the controller parameters based on retrieval of old information, without the need to fully relearn each time. This approach has been tested on experimental set-ups of a flexible beam and of a flexible two-link robot arm, but it is directly applicable to other processes, for instance, in the (petro) chemical industry.

Observer Design in the Tracking Control Problem of Robots

Abstract Full state feedback is the starting point for the majority of currently available control methods for rigid robots, an assumption that hardly can be realized in practice due to the poor quality of velocity measurements. This note considers the tracking control problem of robots using only position measurements. Some known state feedback controllers are modified by integrating a velocity observer in the loop, thereby yielding an exponentially stable closed-loop system without the need for high gain assumptions. The removed requirement for velocity measurements, and consequently for expensive velocity data-acquisition hardware, makes the presented control methods interesting in particular from an economic point of view.

INTELLIGENT ADAPTIVE CONTROL OF MODE-SWITCH PROCESSES

Abstract The intelligence of controllers has increased over the decades. However, the number of applications of adaptive controllers is still restricted, due to practical limits of the implemented continuous adaptation. For processes which operate only in a limited number of modes (so called mode-switch processes), constant adaptation is not needed or desired. In this paper an intelligent extension of adaptive control will be presented, in which process behaviour can be stored in a memory, retrieved from it and evaluated for each mode of operation. This intelligent memory concept leads to an adaptive control structure which, after a learning phase, quickly adjusts the controller parameters based on retrieval of old information, without the need to relearn every time. This approach has been tested on a simulation model of an assembly robot, but it is directly applicable to many processes in the (petro)chemical industry.

Adaptive ‘PD+’ Control of Rigid Robot Manipulators

Abstract Two adaptive trajectory tracking controllers for rigid robot manipulators are presented. These controllers are characterized by three parts, a linear PD part, a nonlinear PD part, and a nonlinear model based part. Asymptotic trajectory tracking can be guaranteed for the closed loop system under quite general conditions on the linear controller gains. Both controllers have the property that they reduce to gravitation compensation and PD control in the particular case of position control. An interesting consequence of this property is that the presented controllers are robust to noise on the velocity measurements, which usually causes parameter drift. This feature of the controllers is demonstrated in a simulation study of a two DOF robot system, in which it is also shown that a well-known adaptive tracking controller from literature suffers from this parameter drift.

Time-Varying Parameter Estimation Combining Directional and Uniform Forgetting

Abstract The paper starts with a unified description of uniform and directional forgetting of old information only and of incoming information also, clarifying the mutual differences. Based on this unification, a new method is introduced. Compared to uniform forgetting, the novel method (like directional forgetting) forgets the same amount of information in the direction of incoming information, but (unlike directional forgetting) it forgets also a fraction of the information in other directions. This frac ti on is determined from UD-decomposition of the covariance matrix, such that directional forgetting prevails when the probability of covariance blow-up is high. The proposed method is able to follow fast parameter variations with low probability of covariance blow-up. This method as well as known methods have been applied to simulations of a two-parameter process with systematic combinations of constant, gradually changing and suddenly changing parameters, for several signal-to noise ratios. The mean squared parameter estimate error without covariance blow-up appeared to be the lowest for the new method.

Self-Tuning Optimal Robust Integrating Pole-Placement Control

Abstract At each sample, a polytope of guaranteed bounds is estimated for the process parameters in the presence of a bounded disturbance, and an optimal robust pole-placer is designed. The control design minimizes the summed squared distances between the coefficient vector of the closed loop polynomials for the vertices of the process parameter poly tope and that for a desired polynomial. Steady-state errors due to the parameter uncertainty are averaged out or eliminated by an integrator at the cost of a lower bandwidth of the controlled system. The benefits of the algorithms are illustrated by simulations for a first-order process.

State-feedback controller for a two-degree-of-freedom flexible robot arm

Abstract This paper describes the control of a two-degree-of-freedom flexible robot arm. The controller design is based on a simplified model, which consists of a number of interacting submodels. The submodel for a flexible link consists of an infinite number of vibration modes. When a steady-state correction for the higher modes is introduced, it is possible to model the low-frequency behaviour correctly with only a limited number of modes in the model. The controller design is based on a simplified model. In this simplified model the Coriolis and centrifugal forces and nearly all steady-state corrections are disregarded. However, the coupling between the vibrations in the two links is taken into account. Experimental results of a laboratory set up demonstrate the feasibility of the proposed algorithm.

Modeling and Control of a Flexible Robot Link

When a flexible link is rotated around an axis, vibrations occur in the link. This paper describes a controller that is able to control the end-position of the link. The flexible link is modelled in state space. It is shown that the model is of infinite order. A method is given for reducing this model to a finite-order model, for which a controller can be designed. A number of experiments is carried out to demonstrate the performance of the controller.

Improved Self-tuning Control with Linear Input Constraints

Abstract First a direct one-step-prediction adaptive minimum-variance controller for ARMAX models with unknown noise parameters is derived. Its parameter estimation explicitly minimizes the covariance of the a-posteriori adaptation error. Theoretically derived convergence conditions are confirmed by simulations with gradually or suddenly time-varying parameters. For amplitude-constrained input signals. it is simple and fast to calculate an unconstrained optimal minimum-variance control signal and subsequently constrain it whenever it is beyond the bounds. In that case. usually old calculated optimal control signal values are replaced by constrained actual ones. However. in that case the predicted output signal will no longer follow the reference signal and hence the replacement of the predictor by the reference signal no longer guarantees minimum variance control and good estimation. In this paper it is demonstrated that constrained minimum-variance control requires the replacement of former reference signal values by former output predictions. The improved control behavior is demonstrated by simulations. A similar replacement in the identification data vector also yields better estimation and hence better adaptation

Comparison of Control Algorithms for Flexible Beam and Robot Arm

Abstract This paper describes the modelling and control of two flexible structures. The first one is a flexible beam moving in the horizontal plane. The second one is a robot arm with flexible links moving in the vertical plane. Both structures are modelled by a limited number of vibrational modes and a steady-state correction. Both are controlled by controllers neglecting the flexibility, by linear controllers taking the flexibility into account for a single parameter set, by linear robust controllers, and by adaptive control according to a mode-switch concept using linear models. The results are better in this order.