This paper deals with the discrete time control of an omnidirectional mobile robot subject to transport delays. A discrete-time model of the vehicle is obtained by considering an exact discretization of the continuous time model of the robot where the time delay induced by a communication network is considered. The path-tracking problem is addressed by means of a prediction strategy based on the well known Smith predictor compensator. The nonlinear nature of the omnidirectional mobile robot induces an approximate estimate of the future values of the systems that are used together with a feedback linearization approach to solve the tracking problem.
Chemical processes with recycling commonly contain delays in both the forward and the backward paths. The characteristic equation of such systems is a quasipolynomial function, so that the corresponding transfer function contains an infinite number of poles. This feature precludes the use of classical stability analysis and control design techniques. In this work, a simple and effective methodology to derive an approximate discrete-time model for continuous-time recycling processes with delay is proposed. The method is based on the discretization, via a fictitious sampler and hold device, of the internal delayed signal, resulting in a finite-dimensional discrete-time version of the original continuous model. In this way, standard analysis methods, such as root locus and stability margin techniques, can be easily applied to the approximate model to obtain some conclusions on the stability of the original recycling process. Illustrative examples are used to show that some stability measures (e.g., stability margin) obtained with the approximate discrete-time model closely describe the behavior of the original recycling process.
Abstract:In this work the problem of stabilization and control for recycling system is considered. Such class of systems is characterized by possessing two main paths named through this work as the direct (feedforward) and the recycling feedback) paths. This work considers recycling systems composed by a system of order n with one unstable pole at the direct path and a stable system of order m in the recycling path, both with different time delays. Two different dynamic delayed controllers are proposed in order to achieve a stable behavior of the closed-loop system. Stability conditions for the existence of these controllers are stated. The problems of step tracking and reject step disturbances are also addressed.
This work considers the stabilization problem for unstable linear input-delay systems. The main idea of the
paper is to use a finite-dimensional approximation for the delay operator, which is based on non-overlapping
partitions of the time delay. Subsequently, each individual delay is approximated by means of a classical
Pade approximation, where the overall approximation results in a high-order Pade approximation that converges
to the original delay operator. By departing from a state-space realization of the approximate process, a linear
observer is used to estimate the delay-free output, which is used within a compensation scheme to stabilize
the process output. The resulting control strategy has the structure of an observer-based Smith prediction
scheme. Numerical results on three examples show that (i) the finer the time delay partition, the better the
control performance and (ii) high-order compensators can be required to stabilize certain unstable processes.
Exponential polynomials arising in transfer functions of chemical processes with recycle and time-delay preclude the use of standar control technics designed for free-delay systems. In this work a simple and effective methodology to derive an approximate discrete-time model free of delay of a continuous timedelayed systems describing recycle and dead-time processes is proposed. The method is based on the discretization of a sampled version of the time-delay term in the original continuous model. Copyright c°2005 IFAC
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