Pilot Plant Evaporator Research Articles

Parametric output feedback controller design

A parameterization of fixed gain output feedback controllers which will assign a complete set of distinct eigenvalues to a given state-space system is presented. The main result is a compact parametric expression for the output feedback controller gain matrix explicitly characterized by two sets of free parameters: the set of n closed-loop system eigenvalues and a set of mr − n design parameters for n-state, r-input, m-output systems. The free design parameters are determined by a sequential design procedure which automatically satisfies the basic orthogonality constraints on the left and right closed-loop eigenvectors under the condition m + r > n. The principal benefits of the explicit characterization of a parametric class of output feedback controllers lie in the ability to directly accommodate various different design criteria. An illustration of the parametric output feedback design procedure is given by way of approximating the optimal full state regulator response of a fifth-order pilot plant evaporator model.

Practical Evaluation of Geometric Control

The multivariable control of a two effect pilot plant evaporator are considered. The two disturbances are inlet flow and inlet concentration. These disturbances must not reach the output which is output concentration and hold up in second effect. The object is to create disturbance rejection by application of geometric control.Based on a linearized model the geometric approach is applied to the design problem. The resulting disturbance rejecting control system is, however, not stable so two feedback loops are further added. This control system is evaluated through simulation of and practical experimentation on the pilot plant. The main result is a complete rejection in the output of the disturbances in the input. Since not all elements in the feedback matrix are assigned in this controller it is further evaluated what results can be obtained through pole assignment. These results are presented both from simulation and experimentation.

Experimental Evaluation of Controllers Designed for Disturbance Localization and Asymptotic Setpoint Tracking

A simple and practical method of designing state feedback, feedforward and setpoint controllers to achieve simultaneous disturbance localization with asymptotic tracking of constant setpoints is described in this paper. The starting point for the solution of this combined problem is the structural result presented by the authors in [6] that express the property of undisturbability in terms of the structure of the coefficient matrices of the state space model and equivalently of the corresponding eigenvector matrix. Simulation and experimental application of the design technique to an 11th order distillation column model, and a computer controlled, pilot-plant evaporator show that the controllers are robust, and comparable to controllers designed using optimal control techniques.

Design and experimental evaluation of controllers for process undisturbability

AbstractSelected state and/or output variables can be made undisturbable, i.e., invariant, to arbitrary, unmeasured changes in specific input variables by properly designed feedback and feedforward controllers. Simulation and experimental applications to a computer‐controlled, pilot plant evaporator gave results superior to conventional controllers.Necessary and sufficient conditions for undisturbability are expressed in terms of the structure of the coefficient matrices of the state space model and equivalently of the corresponding eigenvector matrix. The design procedure normally includes arbitrary specification of all closed‐loop eigenvalues and up to r elements of each eigenvector, where r is the number of control (manipulated) variables.

Multiloop, feedforward, modal and optimal control of an evaporator

The goodness of the ‘classical’ multiloop, dynamic feedforward, modal and optimal control methods, as approaches to multivariable regulatory control, are evaluated on the basis of the experience obtained by designing and experimentally implementing control systems on a double effect pilot plant evaporator. A fifth order state space model is used in the theoretical designs. The criteria used in evaluating the goodness of a control method are the soundness of its principles, its synthesis power and the demands for sophistication in actual implementation.

Time-Optimal Computer Control of a Pilot Plant Evaporator

This paper describes the implementation of time-optimal feedback control on a pilot plant evaporator. The time-optimal control for a time invariant linear system is found using an algorithm which is a combination of a Linear Programming scheme and a Gauss- quadrature formula. The execution speed and core storage requirement of the algorithm allows implementation even on a small on-line computer.Experimental results showed that the time-optimal control system was sensitive to process noise and linearisation errors. The influence of process noise was eliminated by the use of a Kalman filter.

An experimental evaluation of state estimation in multivariable control systems

This paper describes the application of two state estimation techniques, Kalman filters and Luenberger observers, to a computer-controlled pilot plant evaporator. The estimation techniques are used to provide state estimates for an optimal feedback control system and are evaluated using both simulated and experimental data.

MODEL REFERENCE ADAPTIVE CONTROL BASED ON LIAPUNOV'S DIRECT METHOD Part II: Hybrid Computer Simulation and Experimental Application

Abstract A Model Reference Adaptive Control (MRAC) system is evaluated via hybrid computer simulation and experimental application to a computer-controlled, pilot plant evaporator. In both the simulation and experimental studies, the MRAC system performed well and was insensitive to unmeasured process disturbances, to the choice of the initial control policy and to changes in plant operating conditions. In addition to providing an algorithm for adapting control systems to accommodate changing process parameters, MRAC also provides a systematic approach for tuning or developing multivariable control systems for time-invariant processes.

Heat transfer to an immiscible liquid mixture and between liquids in direct contact

Heat transfer to a mixture of two immiscible liquids has been studied in connection with the development of a process for the desalination of sea water. The liquid system consisted of water and refined mineral oil, produced by BP under the trade name of Energol WM-2. Heat transfer to water drops descending through the mineral oil was also investigated. The drag coefficients of the drops in motion were expressed as a function of the Reynolds number. A good correlation was obtained for the heat transfer coefficient expressing the Nusselt number in terms of the Peclet number. Heat transfer to a mixture of two immiscible liquids in co-current turbulent flow without phase change was extensively studied. Friction factor and heat transfer for the oil-in-water type mixtures were theoretically expressed in terms of the volume fraction of oil. The experimental data checked the theoretical derivation quite satisfactorily. No correlations could be obtained for the water-in-oil systems. Similar studies were made for heat transfer in the laminar and turbulent flow with phase change, using a pilot-plant evaporator. Curves were obtained relating the convective heat transfer coefficient to fluid velocity for the liquid mixtures. It was established that, the heat transfer coefficient in evaporation decreased by velocity in the laminar region, but increased in the turbulent region.

An experimental evaluation of Kalman filtering

AbstractThe effectiveness of the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator. The filter was incorporated into a multivariable, computer control system and resulted in good control despite process and/or measurement noise levels of 10%. The results were significantly better than those obtained when the Kalman filter was omitted or replaced by conventional exponential filters. In this application the standard Kalman filter was reasonably insensitive to incorrect estimates of initial conditions or noise statistics and to errors in model parameters. The filter estimates were sensitive to unmeasured process disturbances. However this sensitivity could be reduced by treating the noise covariance matrices R and Q as design parameters rather than noise statistics and selecting values which result in increased weighting of the process measurements relative to the calculated model states.

EXPERIMENTAL EVALUATION OF OPTIMAL MULTIVARIABLE SERVO CONTROL IN CONJUNCTION WITH CONVENTIONAL REGULATORY CONTROL†

Abstract The problem considered is that of driving a multivariable process controlled by conventional feedback control algorithms, from some initial state, to a specified final state such that a linear performance index is minimized. The formulation is based on a linear, discrete, time-invariant model of the process plus a minimum-time or sum of the absolute errors criterion and is solved using a standard linear programming algorithm. Constraints on the state and/or control variables can be incorporated to guarantee practical, physically realizable control policies. Experimental and simulated results show that the technique is easy to implement, and that the use of different criteria produces significantly different process transients. Experimental data from a computer-controlled, pilot plant evaporator show that the method is practical and produces better results than conventional methods.

Experimental evaluation of optimal, multivariable regulatory controllers with model-following capabilities

The formulation of the optimal, linear, time-invariant, multivariable control problem with quadratic performance index is extended so that the solution includes multivariable integral feedback and model-following capabilities in addition to the normal proportional state feedback. The integral action is produced by augmenting the state vector, and eliminates offsets in selected output variables due to constant disturbance inputs. Inclusion of a setpoint vector in the performance index resulted in relatively high controller gains and a fast process response to step changes in setpoints. However, the “real” model-following approach for implementing step changes in setpoints gave greater design flexibility and reliable process responses. The practicality and excellent performance of control systems developed using this approach is demonstrated by experimental data from a computer-controlled pilot-plant evaporator at the University of Alberta.

Optimal, Multivariable Computer Control of a Pilot Plant Evaporator

An optimal, multivariable control system was designed and implemented on a computer controlled pilot plant evaporator and produced significantly better results than conventional methods.The dynamic behavior of the process was represented by a linear, time-invariant, fifth-order state variable model and a general form of the summed quadratic index was selected as a measure of performance. The optimization problem was formulated such that its solution by discrete dynamic programming generated a proportional - plus - integral control law.Simulated control runs were carried out to demonstrate the effect of weighting the “integral states” and to illustrate the results when more integral control states are added than are permitted by the allowance degrees of freedom.Experimental results from a computer controlled pilot plant evaporator were obtained under both the multivariable system and a typical industrial multiloop control system. The response of the evaporator to sizeable load changes under multivariable control showed a significant improvement. It was of particular interest that excellent control results were obtained on the basis of a process model that was only moderately successful in predicting open loop transients.