Optimal Disturbance Localization in a Continuous Stirred Tank Reactor using Infrequent and Indirect Measurements

After its original formulation in [1], the H ∞-optimization problem has drawn great attention (see e.g. [2]-[12] and the references cited therein). Several approaches have been reported in order to solve this important design problem for a variety of systems types. In particular, the H ∞-control problem for discrete-time and sampled-data singlerate and multirate systems has successfully been treated in the past in [7]-[13]. Generally speaking, when the state vector is not available for feedback, the H ∞-control problem is usually solved, in both the continuous and the discrete-time cases, by the use of dynamic measurement feedback. This approach, however, requires the solution of two coupled algebraic Riccati equations, which is, in general, a hard task. On the basis of these two Riccati equations, it is plausible to compute a dynamic controller which achieves the desired requirements (for details see [10]). Nevertheless, a complete characterization of all controllers satisfying the design requirement is not as yet available. Recently, a new technique is presented, for the solution of the H ∞-disturbance attenuation problem in [13]. This technique is based on multirate-output controllers (MROCs). MROCs contain a multirate sampling mechanism with different sampling period to each system measured output. The technique proposed in [13], in order to solve the sampled-data H ∞-disturbance attenuation problem relies mainly on the reduction, under appropriate conditions, of the original H ∞-disturbance attenuation problem, to an associated discrete H ∞-control problem for which a fictitious static state feedback controller is to be designed, eventhough state variables are not available for feedback. This fact has beneficial impact on the theoretical and the numerical complexity of the problem, since using the technique reported in [13], only one algebraic Riccati equation is to be solved, as compared to two algebraic Riccati equations needed by other well known H ∞-control techniques. Another key feature of the approach proposed in [13] is the ability of choosing, under appropriate conditions, the dynamics of the MROC arbitrarily. Thus, strong stabilization can be assured using MROCs without imposing the parity interlacing property requirement in the system under control. In process industry, it is often difficult (or impossible) to measure product qualities as often as desired for control purposes. Indirect information like temperature and pressure is therefore mostly used to control theprocess. Sampled measurements, for example, from laboratory analysis, are, however, often available. For example, in many reaction process, the temperature is given every sampling interval, …