We consider the problem of tuning a closed-loop linear controller for a continuous-time linear, lumped, exponentially stable plant using measurements. A two-step tuning method is proposed based on an “internal model” controller structure. The motivation for developing the method is to reduce the effect of modeling error on the design and to reduce the amount of computation required compared to a similar design performed off-line.

The first step is to solve a controller design problem formulated as a sequence of convex optimization problems in which the cost and constraint functionals and their descent directions are computed directly from plant measurements. The designer is comfortable in specifying desired performance by adjusting the weights of a weighted-max cost function composed of a wide range of time and frequency domain performance functionals.

To implement the “internal model” controller, a plant model is obtained in the second step. The identification objective makes the plant model depend on the desired closed-loop performance. To ensure a robust design, the model satisfies a worst-case error bound which depends on information about the plant, the experiment duration, the noise level, and the order of the model.