General Convex Integral Control
Tóm tắt
In this paper, a fire-new general integral control, named general convex integral control, is proposed. It is derived by defining a nonlinear function set to form the integral control action and educe a new convex function gain integrator, introducing the partial derivative of Lyapunov function into the integrator and resorting to a general strategy to transform ordinary control into general integral control. By using Lyapunov method along with the LaSalle’s invariance principle, the theorem to ensure regionally as well as semi-globally asymptotic stability is established only by some bounded information. Moreover, the lemma to ensure the integrator output to be bounded in the time domain is proposed. The highlight point of this integral control strategy is that the integral control action seems to be infinity, but it factually is finite in the time domain. Therefore, a simple and ingenious method to design the general integral control is founded. Simulation results showed that under the normal and perturbed cases, the optimum response in the whole control domain of interest can all be achieved by a set of control gains, even under the case that the payload is changed abruptly.
Tài liệu tham khảo
H. K. Khalil. Universal integral controllers for minimumphase nonlinear systems. IEEE Transactions on Automatic Control, vol. 45, no. 3, pp. 490–494, 2000.
N. J. Krikelis, S. K. Barkas. Design of tracking systems subject to actuator saturation and integrator windup. International Journal of Control, vol. 39, no. 4, pp. 667–682, 1984.
R. Hanus, M. Kinnaert, J. L. Henrotte. Conditioning technique, a general anti-windup and bumpless transfer method. Automatica, vol. 23, no. 6, pp. 729–739, 1987.
Y. B. Peng, D. Varanceic, R. Hanus. Anti-windup, bumpless, and conditioned transfer techniques for PID controllers. IEEE Control Systems Magazine, vol. 16, pp. 48–57, 1996.
Y. Y. Cao, Z. L. Lin, G. W. David. Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances. Automatica, vol. 40, no. 7, pp. 1221–1228, 2004.
N. Marchand, A. Hably. Global stabilization of multiple integrators with bounded controls. Automatica, vol. 41, no. 12, pp. 2147–2152, 2005.
S. Seshagiri, H. K. Khalil. Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators. Automatica, vol. 41, no. 1, pp. 43–54, 2005.
K. Johanastrom, L. Rundquist. Integrator windup and how to avoid it. In Proceedings of the American Control Conference, IEEE, Pittsburgh, USA, pp. 1693–1698, 1989.
S. M. Shahruz, A. L. Schwartz. Design and optimal tuning of nonlinear PI compensators. Journal of Optimization Theory and Applications, vol. 83, no. 1, pp. 181–198, 1994.
A. S. Hodel, C. E. Hall. Variable-structure PID control to prevent integrator windup. IEEE Transactions on Industrial Electronics, vol. 48, pp. 442–451, 2001.
S. M. Shahruz, A. L. Schwartz. Nonlinear PI compensators that achieve high performance. Journal of Dynamic Systems, Measurement and Control, vol. 119, no. 1, pp. 105–110, 1997.
R. Kelly. Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions. IEEE Transactions on Automatic Control, vol. 43, no. 7, pp. 934–938, 1998.
S. Tarbouriech, C. Pittet, C. Burgat. Output tracking problem for systems with input saturations via nonlinear integrating actions. International Journal of Robust and Nonlinear Control, vol. 10, no. 6, pp. 489–512, 2000.
B. G. Hu. A study on nnonlinear PID controllers—proportional component approach. Acta Automatica Sinica, vol. 32, pp. 219–227, 2006.
C. Q. Huang, X. F. Peng, J. P. Wang. Robust nonlinear PID controllers for anti-windup design of robot manipulators with an uncertain Jacobian matrix. Acta Automatica Sinica, vol. 34, no. 9, pp. 1113–1121, 2008.
B. S. Liu, B. L. Tian. General integral control. In Proceedings of the International Conference on Advanced Computer Control, IEEE, Singapore, pp. 138–143, 2009.
B. S. Liu, B. L. Tian. General integral control design based on linear system theory. In Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, IEEE, Washington DC, USA, pp. 1958–1961, 2012.
B. S. Liu, B. L. Tian. General integral control design based on sliding mode technique. In Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, IEEE, Washington DC, USA, pp. 3244–3247, 2012.
B. S. Liu, J. H. Li, X. Q. Luo. General integral control design via feedback linearization. Intelligent Control and Automation, vol. 5, no. 1, pp. 19–23, 2014.
B. S. Liu, X. Q. Luo, J. H. Li. General concave integral control. Intelligent Control and Automation, vol. 4, no. 4, pp. 356–361, 2013.
H. K. Khalil. Nonlinear Systems, Beijing: Electronics Industry Publishing, 3rd ed., pp. 126–128, 482–484, 2007.