Pedro Albertos

Iterative Identification and Control

In this chapter, we first review the changing role of the model in control system design over the last fifty years. We then focus on the development over the last ten years of the intense research activity and on the important progress that has taken place in the interplay between modelling, identification and robust control design. The major players of this interplay are presented; some key technical difficulties are highlighted, as well as the solutions that have been obtained to conquer them. We end the chapter by presenting the main insights that have been gained by a decade of research on this challenging topic. 1.1 A not-so-brief Historical Perspective There are many ways of describing the evolution of a field of science and engineering over a period of half a century, and each such description is necessarily biased, oversimplified and sketchy. But I have always learned some new insight from such sketchy descriptions, whoever the author. Thus, let me attempt to start with my own modest perspective on the evolution of modelling, identification and control from the post-war period until the present day. Until about 1960, most of control design was based on model-free methods. This was the golden era of Bode and Nyquist plots, of Ziegler-Nichols charts and lead/lag compensators, of root-locus techniques and other graphical design methods. From model-free to model-based control design The introduction of the parametric state-space models by Kalman in 1960, together with the solution of optimal control and optimal filtering problems in a Linear Quadratic Gaussian (LQG) framework [90,91] gave birth to a tremendous development of model-based control design methods. Successful applications abounded, particularly in aerospace, where accurate models were readily available. From modelling to identification The year 1965 can be seen as the founding year for parametric identification with the publication of two milestone papers. The paper [80] set the stage for state-space realisation theory which, twenty-five years later, became the major stepping stone towards what is now called subspace identification. The paper [12] proposed a Maximum Likelihood (ML) framework for the identification of input-output (i. e., ARMAX) models that gave rise to the celebrated

Brief paper: Dual-rate adaptive control

An operator, called the dual-rate transfer function, describing a dual-rate discretized continuous-time system is presented. It can be easily related to single-rate transfer functions of the same system, and its parameters can be experimentally estimated. Based on these models, two adaptive control strategies are outlined, and some results are illustrated by a simple example.

Model-based multirate controllers design

In many industrial control applications the control action updating can be faster than the output measurement, leading to multirate controllers. In this paper, some dual rate operations are used to model the controller as well as the controlled plant. The controller design is model-based and depends on the input to be tracked. The controller is split into two parts acting at different sampling rates and its design is approached based on the characteristics of each available sampling rate. The control target is to reach the similar performances to those the faster single rate controller would achieve. Model-based cancellation controllers are designed using this approach and promising results are obtained.

Brief Paper: Output prediction under scarce data operation: control applications

The problem of estimating the output in missing-data situations is addressed, in case a process model is present. A simple algorithm is presented that uses the input-output model (difference equation), replacing the unknown past values by estimates when necessary. It is compared to state-space approaches such as time-varying Kalman filtering. The analysis of its convergence is carried out for the particular case of dual-rate scarce sampling patterns. The effects of disturbances are also studied. The use of extended order models allows the design of the desired error dynamics. Applications such as parameter estimation and the control under scarce data operation are outlined.

Real-time control of non-uniformly sampled systems

Abstract Industrial applications of digital control require a synergy between well-designed control algorithms and carefully implemented control systems. The design of digital controllers should not be constrained to the simplest case of a single rate with sychronous sampling strategies, and the digital implementation should take account of the actual real-time operating environment. In this paper, control design techniques under non-uniform sampling schemes are reviewed, and computer improvements to cancel or reduce the effect of delays and process interactions are presented.

Brief Recursive identification under scarce measurements - convergence analysis

In this paper, the problem of recursive identification under scarce-data operation is addressed. The control action is assumed to be updated at a fixed rate, while the output is assumed to be measured synchronously with the input update, but with an irregular availability pattern. Under these conditions the use of pseudo-linear recursive algorithms is studied. The main result is the convergence analysis for the case of regular but scarce data availability. The existence of wrong attractors is demonstrated, and a local stability condition of the identification algorithm is derived.

RT control scheduling to reduce control performance degrading

In the framework of real-time digital control, two fundamental parameters are defined, the control effort and the control action interval. The first one is related to the strength of the control that, due to the intersampling open-loop control, determines the degrading of performances under unexpected delays. The second one refers to the unavoidable delays in the multitasking environment due to interactions among the tasks. As a consequence, the scheduling policy should consider not only the tasks delays but also their influence in the control loop behavior, being calculated to minimize the overall degrading of performances.

Simple Real-time Attitude Stabilization of a Quad-rotor Aircraft With Bounded Signals

In this paper, a simple control algorithm to stabilize the attitude of a quad-rotor aircraft is presented. The controller is obtained using the backstepping technique and adding saturation functions. The analysis of convergence is carried out by using the Lyapunov analysis. The performance of the controller with respect to a classical PD controller is compared by simulation. The robustness of the control algorithm with respect to aggressive perturbations is illustrated with real-time experiments

On generalized predictive control: two alternative formulations

Two alternative solutions to the generalized predictive control (GPC) design problem are given for the case when the output horizon is larger than or equal to the plant order. First, using multirate models of the discrete-time plant, we present a state-space solution that does not require state observers or Riccati equation iterations for its implementation. Second, it is shown, via simple algebraic manipulations, that the key prediction equation used for GPC can be easily derived from the transfer function coefficients effectively replacing the Diophantine equation recursions by the inversion of a lower triangular matrix.

Reducing Delays in RT Control: The Control Action Interval

Abstract Industrial application of digital control requires the synergy between well designed control algorithms and carefully implemented control systems. The design of digital controllers considers different parameters when selecting the appropriate algorithms. However, the control performances can be reduced if the system is implemented with several control loops (tasks) which are not considered in the design phase. In this paper, we analyze the control theory and the effects of the multitasking control loops from the data acquisition and output actuation. The paper shows how the output actuation can vary significantly and proposes a method to reduce the jitter effects and the parameters to schedule the tasks. This reduced action interval (Control Action Interval) can be considered in the control design phase in order to properly adjust the control algorithm.