Raymond A. Wright

Nonlinear observer design in the presence of delayed output measurements

The present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements. The proposed nonlinear observer possesses a state-dependent gain which is computed from the solution of a system of first-order singular partial differential equations, and in particular, consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time-instants within the time-delay window introduced by the available output measurements. Therefore, the proposed nonlinear observer exhibits a chain-like structure that explicitly reflects and takes into account the magnitude of the output delay. Furthermore, a set of conditions is derived under which convergence of the estimation error to zero is established. Finally, the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example.

Output feedback control of nonminimum-phase nonlinear processes

This work concerns the development of a general framework for the analysis and output feedback control of open-loop stable nonminimum-phase nonlinear processes. A Smith-type abstract operator structure is introduced, allowing the reduction of the controller synthesis problem for non- minimum-phase processes to the one for minimum-phase processes. State-space methods are used to derive a reduced-order output feedback controller that induces a desired input/output behavior for processes with unstable inverse dynamics and deadtime. The underlying structure of the reduced-order controller is also identified and studied. Finally, an example from a class of chemical reaction systems with nonminimum- phase characteristics is used for evaluating the performance and robustness of the developed control method.

On-line identification and nonlinear control of an industrial pH process

Abstract The control of pH for industrial processes is a highly nonlinear and challenging problem, especially when the nonlinearity is unknown and time-varying. In this work, a controller is developed and implemented for an industrial pH process with unknown chemical composition. The method used is an application of a general algorithm for pH processes, which is based on a representation of the nonlinearity that leads to on-line identification of a small number of parameters. The results show good performance of the pH control algorithm under normal operating conditions and satisfactory performance during several unusual hardware or process problems.

Optimal controller tuning for nonlinear processes

The present work proposes a systematic methodology for the optimal selection of controller parameters in the sense of minimizing a performance index, which is a quadratic function of the tracking error and the control effort. The performance index is calculated explicitly as an algebraic function of the controller parameters by solving Zubovs partial differential equation (PDE). Standard optimization techniques are then employed for the calculation of the optimal values of the controller parameters. The solution of Zubovs PDE is also used to estimate the closed-loop stability region for the chosen values of the controller parameters. The proposed approach is finally illustrated in a chemical reactor control problem.

On-Line Identification and Nonlinear Control of pH Processes

The control of pH is widely recognized as a difficult problem. A novel method for representing the nonlinearity of pH processes is developed. A system with several chemical species of unknown concentrations and with pK values in a certain range is viewed as a piecewise continuous distribution instead of a series of impulses. On-line identification of a small number of parameters can then be used to affect the nonlinearity over an arbitrary pH range. The proposed method applies to systems with varying degrees of chemical knowledge. Computer simulations for two systems demonstrate the performance of this method.

Nonlinear decoupling control in the presence of sensor and actuator deadtimes

This work focuses on synthesizing nonlinear decoupling controllers for multivariable nonlinear systems represented by a state-space model, in the presence of deadtimes. The deadtimes appear in both the inputs and the outputs, but not in the states, and are physically associated with sensors and actuators. Simple sufficient conditions for feasibility of closed-loop deadtimes are derived, which rely only on the structural properties of the system. A control law is then derived so that the closed-loop system is input/output linear and decoupled, with deadtimes equal to the smallest ones that satisfy the feasibility conditions. The proposed method is applied to a chemical process. Its performance is evaluated through simulation in the presence of set-point and disturbance changes.

OPTIMAL CONTROLLER TUNING FOR NONLINEAR PROCESSES

Abstract This work proposes a systematic methodology for the optimal selection of controller parameters, in the sense of minimizing a performance index which is a quadratic function of the tracking error and the control effort. The performance index is calculated explicitly as an algebraic function of the controller parameters by solving a Zubov-type partial differential equation. Standard nonlinear programming techniques are then employed for the calculation of the optimal values of the controller parameters. The solution of the partial differential equation is also used to estimate the closed-loop stability region for the chosen values of the controller parameters. The proposed approach is illustrated in a chemical reactor control problem.

Nonlinear observer design for the slow states of a singularly perturbed system

Abstract The present work proposes a new approach to the nonlinear observer design problem in the presence of two-time-scale multiplicity. In particular, nonlinear processes are considered that exhibit fast and unmeasurable slow dynamic modes, and the latter need to be accurately reconstructed through the use of a state observer. The proposed observer is designed on the basis of the reduced-order process dynamics that evolve on the system’s slow manifold, and the dynamic behavior of the estimation error is analyzed and mathematically characterized in the presence of the unmodeled fast process dynamics. It is shown, that within the proposed nonlinear observer design framework, the observation error generated by neglecting the fast process dynamics is of order O ( ɛ ) , where ɛ is the perturbation parameter and a measure of the relative speed/time-constant of the fast and the slow component of the process dynamics. Furthermore, the analysis conducted establishes robustness of the proposed observer design method with respect to fast unmodeled process dynamics. Finally, the performance of the proposed method and the convergence properties of the reduced-order nonlinear observer designed are evaluated in an illustrative biological reactor example.

Model-based synthesis of nonlinear PI and PID controllers

Abstract PI and PID controllers continue to be popular in industrial applications. It is well known that linear PI and PID controllers result from the application of model-based controller design methods to linear first and second-order systems. This work shows that nonlinear PI and PID controllers result from application of nonlinear controller design methods to nonlinear lirst and second-order systems. Examples illustrating nonlinear PI and PID controllers are given for chemical process models.

pH Control in the Presence of Precipitation Equilibria

Abstract The control of pH to minimize solubility of precipitates is a challenging problem. A first principles model for a precipitation process, including acid/base equilibria and precipitation equilibria is developed. A minimal order realization of the full order model is derived, which consists of linear first-order dynamics and a static nonlinearity in the output map. The control problem becomes linear after it is redefined in terms of an equivalent output. The approach is illustrated in a zinc hydroxide precipitation example.