H2/H∞ output information-based disturbance attenuation for differential linear repetitive processes

Repetitive processes propagate information in two independent directions where the duration of one is finite. They pose control problems that cannot be solved by application of results for other classes of 2D systems. This paper develops controller design algorithms for differential linear processes, where information in one direction is governed by a matrix differential equation and in the other by a matrix discrete equation, in an H2/H∞ setting. The objectives are stabilization and disturbance attenuation, and the controller used is actuated by the process output and hence the use of a state observer is avoided

<i>H</i>₂ and mixed <i>H</i>₂/<i>H</i>_∞ Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control

H∞ and guaranteed cost control of discrete linear repetitive processes

AbstractRepetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. In general, they cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here first we give major new results on the design of control laws using an H∞ setting and including the possibility of uncertainty in the process model. Then we give the first ever results on guaranteed cost control, i.e. including a performance criterion in the design. The designs in both cases can be computed using linear matrix inequalities. These results are for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control

Iterative learning fault-tolerant control for differential time-delay batch processes in finite frequency domains

This paper develops a fault-tolerant iterative learning control law for a~class of~linear time-delay differential batch processes with actuator faults using the repetitive process setting. Once the dynamics are expressed in this setting, stability analysis and control law design makes use of the generalized Kalman-Yakubovich-Popov (KYP) lemma in the form of the corresponding linear matrix inequalities (LMIs). In particular, sufficient conditions for the existence of a fault-tolerant control law are developed together with design algorithms for the associated matrices. Under the action of this control law the ILC dynamics have a monotonicity property in terms of an error sequence formed from the difference between the supplied reference trajectory and the outputs produced. An extension to robust control against structured time-varying uncertainties is also developed. Finally, a simulation based case study on the model of a~two-stage chemical reactor with delayed recycle is given to demonstrate the feasibility and effectiveness of the new designs

Output Information Based Fault-Tolerant Iterative Learning Control for Dual-Rate Sampling Process with Disturbances and Output Delay

For a class of single-input single-output (SISO) dual-rate sampling processes with disturbances and output delay, this paper presents a robust fault-tolerant iterative learning control algorithm based on output information. Firstly, the dual-rate sampling process with output delay is transformed into discrete system in state-space model form with slow sampling rate without time delay by using lifting technology; then output information based fault-tolerant iterative learning control scheme is designed and the control process is turned into an equivalent two-dimensional (2D) repetitive process. Moreover, based on the repetitive process stability theory, the sufficient conditions for the stability of system and the design method of robust controller are given in terms of linear matrix inequalities (LMIs) technique. Finally, the flow control simulations of two flow tanks in series demonstrate the feasibility and effectiveness of the proposed method