Kalman-designed algorithm

Therefore, the Kalman designed algorithm is specified by obtaining the modified Z-transform of the process pulse transfer function ot get P(z) and Q(z) and then substituting these values into equation (19). 

In this work, an Extended Kalman Filter (EKF), an extension of the Kalman Filter, is designed to reconstruct the current state variables from the delayed state measurement. The advantage of the EKF is that it requires information only from the previous sampling time and allows prior knowledge of a system via process models to be used for the estimation. The algorithm of the EKF can be seen in Appendix A. 

Typically, one specifies the desired response, C(z)/R(z), which yields from equation (12) the required design of the controller, D(z). In practice, however, this design technique results in a controller which requires excessive valve movement, an undesirable situation. Consequently, Kalman (12) developed a Z-transform algorithm which specifies the desired output, C(z), and the desired valve travel, M(z) for a setpoint change. The desired response and valve travel for a unit step change in setpoint is shown in Figure 22. The system response,... 

Chapter 12 considers the combination of optimal control with state and parameter estimation. The separation principle is developed, which states that the design of a control problem with measurement and model uncertainty can be treated by first performing a Kalman filter estimate of the states and then developing the optimal control law based upon the estimated states. For linear regulator problems, the problem is known as the linear quadratic Gaussian (LQG) problem. The inclusion of model parameter identification results in adaptive control algorithms. 

In chemical process systems engineering, it has been widely acknowledged that the choice of control structure has a profound effect on performance, is much more important than the choice of control algorithm, and it is second only to plant design in importance for effective control [25-28], In a way that is analogous to the choice of control structure in the constructive approach, the choice of estimation structure has been considered to attain robustness via passivation [16-19]. The idea is that the standard Kalman filter (EKF) and Luenberger (L) nonlinear estimators have structures that are fixed by the (possibly ill-conditioned) detectability property of the estimation model, and that robustness-oriented passive estimation structures can be designed for the purpose at hand [19]. 

Heuristic AFAP scheduling, design iteration, the Intel 8251, a Kalman filter example, the FRISC, and a greatest common divisor algorithm example. 

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