Читать книгу PID Passivity-Based Control of Nonlinear Systems with Applications - Romeo Ortega - Страница 31

As shown in Ortega et al. (2008), van der Schaft (2016), Venkatraman and van der Schaft (2010), and Zhang et al. (2015), one way to overcome the dissipation obstacle is to generate relative degree zero outputs. However, it is then not possible to add a derivative term to the controller that, due to its “prediction‐like” feature, is useful in some applications. In Chapter 6, we propose a new construction of PID‐PBC, where it is possible to add a derivative action to systems where the dissipation obstacle is present. We will also show that the integral and derivative terms perform the energy‐shaping process, while the proportional term completes the PBC design by injecting damping into the closed‐loop system.