The project involved the commissioning of the process equipment and the addition of instrumentation and interface to a SCADA system developed in the School of Chemical Engineering. I declare that all work in this dissertation is my own unless otherwise noted and referenced. To the Chemical Engineering workshop staff for their assistance in commissioning the equipment and to Dudley Naidoo for solving the electronic problems.
ADMC
DAS DAE
Chapter 1
Dynamic Matrix Control is one of the most successful predictive modeling schemes and quite popular in the process industry. Also included are the results obtained from off-line tests, as well as the actual application of the ADMC Integrative controller to the 2-input I 2-output subsystem of the Training Plant. Interfacing the system with a SCADA computer system, consisting of real-time simulation and data acquisition software developed at the School of Chemical Engineering.
Chapter 2
As mentioned above in Section 2.2, the training facility shown in Figure 2.2 allows the definition of the relevant slIb system by manipulating some control valves in the equipment. Cheng, Mongkhonsi and Kershenbaum [1997] applied the minimum least squares requirement, i.e. the minimization of the integral of the weighted squared residual errors in the process model and the measuring device, to develop a sequential algorithm for non-linear differential and algebraic systems using calculus of variations. The initial modeling approach for the existing training facility was based on a state-space model that, as described in section A.3.1 (Appendix A), is formulated from first principles.
Chapter 3
The Kalman filter is a stochastic filter that allows the estimation of the states of the system based on a linear state space model. As mentioned above, to estimate the state of the studied training plant using the state space model, an EKF technique was applied. Model-predicted unit step responses for the 2-input, 12-output subsystem of the training plant (M = 5).
Chapter 4
At discrete sampling moments, .1/, the step response coefficients can be determined from the step response model. While increasing N can lead to better control system performance. the manipulated variable motions become larger and there is a reduction in the controller's robustness. In the unconstrained run (Figure 4.6), the control was effective in reducing setpoint deviations, while at the same time it was severe in terms of control movements as the second optimized move makes a correction after the first move, thus creating an "overshoot" move.
Chapter 5
Most adaptive control systems require extensive calculations for parameter estimation and optimal adjustment of controller settings. In this paper, a self-tuning adaptive control scheme is applied to the linear dynamic matrix control algorithm, where the step response coefficients are recursively updated (Chapter 6). As mentioned above, online determination of process parameters is a key element in adaptive control.
In adaptive control, real-time (or sequential) updating of model parameters is more appropriate than batch (non-sequential) processing of input-output data. This technique assumes that the order and shape of the system are known. The initial value of the model was fixed to the measured sequence at the starting point of the sequence.
This is due to measurement errors, inaccuracies in model formulation and non-linearity. In this way, the DMC controller continues to be built from a good local representation of the process. This is based on a weighted combination of the initial step response (x \VI), and the same response delayed one time step (x w}) (Figure 6.2).
Real step responses identified by the regularized model 6 minutes and 49 seconds from the start of the run. Identified step responses using a regularized model in the pump tank plant, 1 hour from the start of the run. Identified step responses based on a regularized model in the pump tank installation, 2 hours, 37 minutes and 30 seconds from the start of the run.
Chapter 7
The control of the output of integrating process units must be considered together with the control of other process outputs, and in the case of constrained variables, all the constraints must be considered simultaneously. The proposed approach does not require the formulation of the MPC problem in the state space, and due to this advantage, it can be directly implemented in the step response fannulation of the DMC algorithm. This scheme takes advantage of the fact that the predicted response due to previous input is a straight line passing through the output at the current control instant.
The slope of the predicted response is thus determined from the slope of the output path between the current and previolence control instants. Recall that the vector of vectors XOPRED contains P identical predictions of the output vector at current time /=0. The vector XpRED contains predictions of the output vector at P points on the future path as contributed by the previous M control movements and the future P control movements.
The terms in the first column will be non-zero for an integrating system, and operate on a non-zero absolute displacement of the control action (sum of all motions), to provide a steady ramp at all integrating outputs of the system add (see equation (7.2»). A scheme for adapting the internal convolution model of an LDMC, by closed-loop recursive identification of the step response coefficients in real time following the methodology presented in Chapter 6, is presented in this section developed for the integrative case For an integration process, the defined lower matrix row of each of the matrices BOL.
If we reduce the datum to -M, the corrected prediction of the current state according to equation (6.4) is therefore given by.
Integrating Adap tive Dvnam ic Matr ix Control
Application of the proposed Integrative LDMC I ADMC was carried out on the Training Plant described in Chapter 2 and schematically represented in Figure 2.2. As mentioned in section 2.5, only a 2-input 12-output subsystem of the Training Plant shown in Figure 2.4 was simulated. As expected, LDMC controller performance was poor, leading to excessive valve work and oscillations in the output responses due to the unexplained integrative nature of the process (Figure 7.3 (a»).
Identified step responses using simulation model, 7 minutes and 10 seconds from the start of the run. The effect of the constraints can be seen in the much slower setpoint tracking where the constraints are active, reducing the controller's performance. The adaptation diagrams presented in Figure 7.10 show the effort of the Adaptive Dynamic Matrix Controller to correctly identify the coefficients of the step responses, albeit with noise and other disturbances affecting the process as found in the off diagonal elements.
As also seen in the off-line simulation (section 7.5.1), adjusting the model parameters reduces the output error. The algorithm written in Matlab was used for state estimation, and based on the estimated data, step responses of the 2·input 12.output subsystem in the training facility were predicted. In the second step, i.e. in the control step, it is usually necessary to recalculate the controller coefficients so that appropriate control action can be derived.
The resulting Integrating Adaptive Dynamic Matrix Control algorithm was finally used in the 2-input I 2-output subsystem of the training plant.
Input variables are those that independently stimulate the system and can thereby cause change in the internal state of the process. Output variables are those through which one obtains information about the internal state of the process. The state variables are therefore the true indicator of the internal state of the system.
Although the output variables are defined as measurements, it is possible that some outputs are not measured on-line (no instrument is installed) in the process, but require that rare samples 10 be sent to the laboratory for analysis. The process variables of a distributed parameter process on the other hand vary with space and time. A process is defined as stable if "self-regulating", that is, the process variables converge to a steady state when disturbed and / Unstable if the variables go to infinity (mathematically).
In general, input/output models arise as a result of appropriate transformations of the state space form, but they can also be obtained directly from the correlation of input/output data. When the process model is formulated from first principles, it often naturally occurs in state space form in the time domain. These models are almost exclusively used for the analysis of non-linear system behavior, because most other model forms can only represent linear dynamic behavior.
When a process is too complex for a theoretical approach (usually because very little information is available about the fundamental nature of the process or because the equations of the theoretical model are extremely complex), an empirical approach ~ is the appropriate choice.
Extended Kalman Filter Formulation
To account for the possibility that y states may also be observed, augment the above equation as follows. The proposal of this appendix is to provide the Matlab algorithm used in Chapter 3 for the outdated estimation of the theoretical process of the training plant model using the extended Kalman filter.
IIH_,
The diagonal responses of the mismatched process model are, the first 2 times and the second Yz of their correct magnitudes. The Integrating Adaptive Dynamic Matrix Control technique developed in the present work was implemented in an existing Linear Dynamic Matrix Control (LDMC) algorithm developed by Mulholland and Prosser [1997] within an adaptive SCADA system at the Faculty of Chemical Engineering.
