This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 2 U+00B3 factorial experimental design for a fractional order proportional integral and derivative controller U+0028 FOPID U+0029, integer order proportional integral and derivative controller U+0028 IOPID U+0029 and the Skogestad internal model control controller U+0028 SIMC U+0029. The factors assumed in experiment are the presence of random noise, external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.

Design and robust performance evaluation of a fractional order PID controller applied to a DC motor

When designing robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.

/pdf/a-partially-augmented-lagrangian-method-for-low-order-h-58zut7c39q.pdf

A partially augmented Lagrangian method for low order H-infinity controller synthesis using rational constraints

This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a partially augmented Lagrangian method. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance and speed.

A Partially Augmented Lagrangian Method for Low Order ${\rm H}$ -Infinity Controller Synthesis Using Rational Constraints

Here we present numerical results and timings obtained using our quasi-Newton interior point method on a set of 44 systems. We were not able to include these results in the article due to limited a ...

Additional Numerical Results for the Quasi-Newton Interior Point Method for Low Order H-Infinity Controller Synthesis

This technicalnote proposesa methodfor loworder H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is thensolvedby applyinga quasi-Newtonprimal-dualinterior pointmethod. The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method has com- parable performance and speed.

http://ieeexplore.ieee.org/iel5/9/5784391/05719547.pdf

H. A. van der Vorst

Papers

A Quasi-Newton Interior Point Method for Low Order H-Infinity Controller Synthesis