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Keywords:
stabilizing control; mixed sensitivity; pole placement; reference tracking; linear systems; robust control; 2DOF control configuration
stabilizing control; mixed sensitivity; pole placement; reference tracking; linear systems; robust control; 2DOF control configuration
Summary:
Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) controllable and observable systems where the controller has access to some plant outputs but not others are considered. Analytical expressions of coprime factorizations of a given plant, a solution of the Diophantine equation and the two free parameters of a two-degrees of freedom (2DOF) controller based on observer stabilizing control are presented solving a pole placement problem, a mixed sensitivity criterion, and a reference tracking problem. These solutions are based on proposed stabilizing gains solving a pole placement problem by output feedback. The proposed gains simplify the coprime factorizations of the plant and the controller, and allow assigning a decoupled characteristic polynomial. The 2DOF stabilizing control is based on the Parameterization of All Stabilizing Controllers (PASC) where the free parameter in the feedback part of the controller solves the mixed sensitivity robust control problem of attenuation of a Low-Frequency (LF) additive disturbance at the input of the plant and of a High-Frequency (HF) additive disturbance at the measurement, while the free parameter in the reference part of the controller assures that the controlled output tracks the reference at LF such as step or sinusoidal inputs. With the proposed expressions, the mixed sensitivity problem is solved without using weighting functions, so the controller does not increase its order; and the infinite norm of the mixed sensitivity criterion, as well as the assignment of poles, is determined by a set of control parameters.
References:
[1] Chilali, M., Gahinet, P: $\mathcal{H_{\infty}}$ design with pole placement constraints: An {LMI} approach. IEEE Trans. Automat. Control 41 (1996), 358-367. DOI | MR 1382985
[2] Desoer, C. A.: Decoupling linear multiinput multioutput plants by dynamic output feedback: An algebraic theory. IEEE Trans. Automat. Control 31 (1986), 744-750. DOI | MR 0848673
[3] Doyle, J. C., Glover, K., Khargonekar, P., Francis, B. A.: State-space solutions to standard $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ control problems. IEEE Trans. Automat. Control 34 (1989), 831-847. DOI | MR 1004301
[4] Folly, K. A.: A Comparison of Two Methods for Preventing Pole-zero Cancellation in ${H}_{\infty}$ Power System Controller Design. IEEE Lausanne Power Tech (2007).
[5] Flores, M. A., Galindo, R.: Robust control for outputs of interest different from the measured outputs, based on the parameterization of stabilizing controllers. Control robusto para salidas de interés diferentes a las medidas, basado en la parametrización de controladores estabilizantes. In: {XVI} Latinamerican Congress of Automatic Control, {CLCA} 2014.
[6] Gahinet, P., Apkarian, P.: A linear matrix inequality approach to ${H}_{\infty}$ control. Int. J. Robust Nonlinear Control 4 (1994), 421-448. DOI | MR 1286148
[7] Galindo, R.: Parameterization of all stable controllers stabilizing full state information systems and mixed sensitivity. In: Proc. The Institution of Mechanical Engineers Part {I}: J. Systems Control Engrg. 223 (2009), 957-971. DOI
[8] Galindo, R.: Input/output decoupling of square linear systems by dynamic two-parameter stabilizing control. Asian J. Control 18 (2016), 2310-2316. DOI | MR 3580390
[9] Galindo, R., Conejo, C. D.: A Parametrization of all one parameter stabilizing controllers and a mixed sensitivity problem, for square systems. In: International Conference on Electrical Engineering, Computing Science and Automatic Control (012, pp. 1-6.
[10] Galindo, R., Malabre, M., Kučera, V.: Mixed sensitivity $\mathcal{H}_{\infty}$ control for {LTI} systems. IEEE Conf. Decision Control 2 (2004), 1331-1336.
[11] Gao, W., Zhang, N., Du, H.: A half-car model for dynamic analysis of vehicles with random parameters. In: Australasian Congress on Applied Mechanics (2007).
[12] Glover, K., McFarlane, D.: Robust stabilization of normalized coprime factor plant descriptions with $\mathcal{H}_{\infty}$-bounded uncertainty. IEEE Trans. Automat. Control 34 (1989), 821-830. DOI 10.1109/9.29424 | MR 1004300
[13] Henrion, D., Šebek, M., Kučera, V.: Robust Pole Placement for Second-Order Systems: An LMI Approach. Kybernetika 41 (2005), 1-14. MR 2130481
[14] Le, X., Wang, J.: Robust Pole Assignment for Synthesizing Feedback Control Systems Using Recurrent Neural Networks. IEEE Trans. Neural Networks Learning Systems 25 (2014), 383-393. DOI 10.1109/TNNLS.2013.2275732
[15] McFarlane, D., Glover, K.: A loop-shaping design procedure using $\mathcal{H}_{\infty}$ synthesis. IEEE Trans. Automat. Control 37 (1992), 759-769. DOI | MR 1164547
[16] Nett, C. N., Jacobson, C., Balas, M. J.: A connection between state-space and doubly coprime fractional representations. IEEE Trans. Automat. Control 29 (1984), 831-832. DOI | MR 0756933
[17] Sarjaš, A., Chowdhury, A., Svečko, R.: Robust Optimal Regional Closed-loop Pole Assignment over Positivity Conditions and Differential Evolution. IFAC CESCIT 48 (2015), 141-146.
[18] Tsai, M. C., Geddes, E. J. M., Postlethwaite, I.: Pole-zero cancellations and closed-loop properties of an ${H}_{\infty}$ mixed sensitivity design problem. Automatica 28 (1992), 519-530. DOI | MR 1166025
[19] Vidyasagar, M.: Control System Synthesis: A Factorization Approach. M.I.T. Press, 1985. MR 0787045
[20] Zhou, K., Doyle, J. C., Glover, K.: Robust and Optimal Control. Prentice Hall, 1995. Zbl 0999.49500
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