Robust synthesis of feedforward compensators

Abstrac

Constrained H̳₂ design via convex optimization with applications

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1998.In title on t.p., double-underscored "H" appears in script.Includes bibliographical references (p. 133-138).A convex optimization controller design method is presented which minimizes the closed-loop H2 norm, subject to constraints on the magnitude of closed-loop transfer functions and transient responses due to specified inputs. This method uses direct parameter optimization of the closed-loop Youla or Q-parameter where the variables are the coefficients of a stable orthogonal basis. The basis is constructed using the recently rediscovered Generalized Orthonormal Basis Functions (GOBF) that have found application in system identification. It is proposed that many typical control specifications including robustness to modeling error and gain and phase margins can be posed with two simple constraints in the frequency and time domain. With some approximation, this formulation allows the controller design problem to be cast as a quadratic program. Two example applications demonstrate the practical utility of this method for real systems. First this method is applied to the roll axis of the EOS-AM1 spacecraft attitude control system, with a set of performance and robustness specifications. The constrained H2 controller simultaneously meets the specifications where previous model-based control studies failed. Then a constrained H2 controller is designed for an active vibration isolation system for a spaceborne optical technology demonstration test stand. Mixed specifications are successfully incorporated into the design and the results are verified with experimental frequency data.by Beau V. Lintereur.S.M

Proceedings of the 3rd Annual Conference on Aerospace Computational Control, volume 1

Conference topics included definition of tool requirements, advanced multibody component representation descriptions, model reduction, parallel computation, real time simulation, control design and analysis software, user interface issues, testing and verification, and applications to spacecraft, robotics, and aircraft

Analysis and design of robust stabilizing modified repetitive control systems

In control system practice, high precision tracking or attenuation for periodic signals is an important issue. Repetitive control is known as an e.ective approach for such control problems. The internal model principle shows that the repetitive control system which contains a periodic generator in the closed-loop can achieve zero steady-state error for reference input or completely attenuate disturbance. Due to its simple structure and high control precision, repetitive control has been widely applied in many systems. To improve existing results on repetitive control theory, this thesis presents theoretical results in analysis and design repetitive control system. The main work and innovations are listed as follows: We propose a design method of robust stabilizing modi.ed repetitive controllers for multiple-input/multiple-output plants with uncertainties. The parameterization of all robust stabilizing modi.ed repetitive controllers for multiple-input/multiple-output plant with uncertainty is obtained by employing H∞ control theory based on the Riccati equation. The robust stabilizing controller contains free parameters that are designed to achieve desirable control characteristic. In addition, the bandwidth of low-pass .lter has been analyzed. In order to simplify the design process and avoid the wrong results obtained by graphical method, the robust stability conditions are converted to LMIs-constraint conditions by employing the delay-dependent bounded real lemma. When the free parameters of the parameterization of all robust stabiliz-ing controllers is adequately chosen, then the controller works as robust stabilizing modi.ed repetitive controller. For a time-varying periodic disturbances, we give an design method of an opti-mal robust stabilizing modi.ed repetitive controller for a strictly proper plant with time-varying uncertainties. A modi.ed repetitive controller with time-varying delay structure, inserted by a low-pass .lter and an adjustable parameter, is developed for this class of system. Two linear matrix inequalities LMIs-based robust stability con-ditions of the closed-loop system with time-varying state delay are derived for .xed parameters. One is a delay-dependent robust stability condition that is derived based on the free-weight matrix. The other robust stability condition is obtained based on the H∞ control problem by introducing a linear unitary operator. To obtain the desired controller, the design problems are converted to two LMI-constrained opti-mization problems by reformulating the LMIs given in the robust stability conditions. The validity of the proposed method is verified through a numerical example.学位記番号：工博甲46

Inversion-based feedforward-feedback control: theory and implementation to high-speed atomic force microscope imaging

In this dissertation, a suite of inversion-based feedforward-feedback control techniques are developed and applied to achieve high speed AFM imaging. In the last decade, great efforts have been made in developing the inversion-based feedforward control as an effective approach for precision output tracking. Such efforts are facilitated by the fruitful results obtained in the stable-inversion theory, including, mainly, the bounded inverse of nonminimum-phase systems, the preview-based inversion method that quantified the effect of the future desired trajectory on the inverse input, the consideration of the model uncertainties in the system inverse, and the integration of inversion with feedback and iterative control. However, challenges still exist in those inversion-based approaches. For example, although it has been shown that the inversion-based iterative control (IIC) technique can effectively compensate for the vibrational dynamics during the output tracking in the repetitive applications, however, compensating for both the hysteresis effect and the dynamics effect simultaneously using the IIC approach has not been established yet. Moreover, the current design of the inversion-based feedforward feedback two-degree-of-freedom (2DOF) controller is ad-hoc, and the minimization of the model uncertainty effects on the feedforward control has not been addressed. Furthermore, although it is possible to combine system inversion with both iterative learning and feedback control in the so-called current cycle feedback iterative learning control (CCF-ILC) approach, the current controller design is limited to be casual and the use of such CCF-ILC approach for rejecting slowly varying periodic disturbance has not been explored. These challenges, as magnified in applications such as high-speed AFM imaging, motivate the research of this dissertation. Particularly, it is shown that the IIC approach can effectively compensate for both the hysteresis and vibrational dynamics effects of smart actuators. The convergence of the IIC algorithm is investigated by capturing the input-output behavior of piezo actuators with a cascade model consisting of a rate-independent hysteresis at the input followed by the dynamics part of the system. The size of the hysteresis and the vibrational dynamics variations that can be compensated for (by using the IIC method) has been quantified. Secondly, a novel robust-inversion has been developed for single-input-single-output (SISO) LTI systems, which minimized the dynamics uncertainty effect and obtained a guaranteed tracking performance for bounded dynamics uncertainties. Based on the robust-inversion approach, a systematic design of inversion-based two-degree-of-freedom (2DOF)-control was developed. Finally, the robust inversion- based current cycle feedback iterative learning control approach was developed for the rejection of slow varying periodic disturbances. The proposed CCF-ILC controller design utilizes the recently-developed robust-inversion technique to minimize the model uncertainty effect on the feedforward control, as well as to remove the causality constraints in other CCFILC approaches. It is shown that the iterative law converges, and attains a bounded tracking error upon noise and disturbances. In this dissertation, these techniques have been successfully implemented to achieve high-speed AFM imaging of large-size samples. Specifically, it is shown that precision positioning of the probe in the AFM lateral (x-y) scanning can be successfully achieved by using the inversion-based iterative-control (IIC) techniques and robust-inversion based 2DOF control design approach. The AFM imaging speed as well as the sample estimation can be substantially improved by using the CCF-ILC approach for the precision positioning of the probe in the vertical direction