Chriss Grimholt

Optimal PI-Control and Verification of the SIMC Tuning Rule

Abstract Optimal PI-settings are derived for first-order with delay processes for specified levels of robustness ( M s -value) and compared with the simple SIMC-rule. Optimality (performance) is defined in terms of the integrated absolute error (IAE) of the output for combined step changes in setpoints and input disturbances. With SIMC, the robustness level is adjusted by changing the tuning parameter τ c , and the SIMC-rule was found to give surprisingly good setting with almost Pareto-optimal performance. The exception is a pure time delay processes where the SIMC-rule gives a pure integral controller with somewhat sluggish response. A simple modification to improve on this, is to increase the time constant in the rule by one third of the time delay.

The SIMC Method for Smooth PID Controller Tuning

The SIMC method for PID controller tuning (Skogestad in J. Process. Control 13:291–309, 2003) has already found widespread industrial usage. This chapter gives an updated overview of the method, mainly from a user’s point of view. The basis for the SIMC method is a first-order plus time delay model, and we present a new effective method to obtain the model from a simple closed-loop experiment. An important advantage of the SIMC rule is that there is a single tuning parameter (τ c ) that gives a good balance between the PID parameters (K c ,τ I ,τ D ) and can be adjusted to get a desired trade-off between performance (“tight” control) and robustness (“smooth” control). Compared to the original paper of Skogestad (J. Process. Control 13:291–309, 2003), the choice of the tuning parameter τ c is discussed in more detail, and lower and upper limits are presented for tight and smooth tuning, respectively. Finally, the optimality of the SIMC PI rules is studied by comparing the performance (IAE) versus robustness (M s ) trade-off with the Pareto-optimal curve. The difference is small, which leads to the conclusion that the SIMC rules are close to optimal. The only exception is for pure time delay processes, so we introduce the “improved” SIMC rule to improve the performance for this case.

A Comparison between Internal Model Control, Optimal PIDF and Robust Controllers for Unstable Flow in Risers

Abstract Anti-slug control of multiphase risers involves stabilizing an open-loop unstable operating point. PID control is the preferred choice in the industry, but appropriate tuning is required for robustness. In this paper, we define PIDF as a PID with a low-pass filter on its derivative action where the low-pass filter is crucial for the dynamics. We compared a new PIDF tuning based on Internal Model Control (IMC), together with two other tunings from the literature, with an optimal PIDF controller. The optimal PIDF tuning was found by minimizing a performance cost function while satisfying robustness requirements (input usage and complementary sensitivity peak). Next, we considered two types of robust ℋ∞ controller (mixed-sensitivity and loop-shaping). We compared the controllers based on their pareto-optimality, and we tested the controllers experimentally. We found that the new IMC-PIDF controllers is the closest to the optimal PIDF controller, but the robustness can be further improved by ℋ loop-shaping.

Optimal PID-Control on First Order Plus Time Delay Systems & Verification of the SIMC Rules

Abstract Optimal PID-settings are found for first-order with delay processes for specified levels of robustness (MS-value) and compared with an extended SIMC-rule. Optimality (performance) is defined in terms of the integrated absolute error (IAE) for combined step changes in load output and input disturbances. The SIMC-rules gives a PI-controller for first order systems and no recommendation is given for tuning the derivative part. We propose an extended SIMC-rule where the the time delay is counteracted by introducing derivative action with τ D = θ/3. The modification was found to give surprisingly good settings with near Pareto-optimal performance. However, to obtain the improvement over PI control τ c should be reduced to about half of the recommended value τ c = θ.

Improved Optimization-based Design of PID Controllers Using Exact Gradients

Abstract Finding good controller settings that satisfy complex design criteria is not trivial, even for the simple three parameter proportional - integral - derivative (pid) controller. One strategy is to formulate the design problem into an optimization problem. However, when using gradient based optimization with finite differences to estimate the gradients, the algorithm often fails to converge to the optimal solution. This is thought to be a result of inaccuracies in the estimation of the gradients. In this paper we show exact gradients for a typical performance ( iae ) versus robustness ( M S , M T ) design problem. We demonstrate increased accuracy in the optimization when using exact gradients compared with forward finite differences.

Estimation of Primary Variables from Combination of Secondary Measurements: Comparison of Alternative Methods for Monitoring and Control

In this work, we propose a method to estimate the primary variables based on a combination of measurements. Our method is a reformulation of the Loss method. We will compare our method with the other well-known estimators.