Optimal and learning-based output tracking with non-periodic tracking-transition
Creators: name: Liu, Jiangbo
Publisher: name: No Publisher Supplied
Year: 2017

description: High-speed precision tracking is needed in a wide variety of motion control applications ranging from high-speed AFM(Atomic Force Microscope) operation, high-throughput manufacturing, to robotic operations. Challenges still exist in high-speed precision control of systems such as smart actuators with coupled hysteresis and dynamics. Although output tracking has been well-studied for linear systems, tracking with non-periodic tracking-transition switching for non-minimum phase linear systems still remains challenging, especially when multiple control objectives need to be achieved, including smooth transition from one output tracking session to the next one without inducing post-transition oscillations, input energy minimization without saturation under input amplitude constraint, and furthermore, minimization of the overall transition time. Moreover, further difficulties also arise in exploring the advantages of iterative learning control (ILC) in achieving precision but robust output tracking at high-speed to non-repetitive applications with online-generated desired trajectory, particularly for systems with complicated input-output behavior such as Hammerstein systems. The ILC framework can be extended, although for linear systems, to non-periodic output tracking via the superposition principle (SP), where the system response (output) to a linear combination of inputs equals to the same linear combination of the outputs to each individual inputs. Exploring the notion of the SP beyond linear systems is largely limited, as the nonlinearities are difficult to be modeled effectively and accurately. Therefore, challenges still exist in high-speed precision output tracking in emerging applications.  In this dissertation, a multi-objective optimal tracking/transition under input constraints for non-periodic tracking/transition switching problem, and a learning-based approach for tracking control of Hammerstein systems are proposed. An approach to extend the previous work on smooth output transition and smooth tracking/transition switching to further achieve minimization of both input-energy and transition time under input amplitude constraints is proposed. The constrained input optimization problem is converted to an unconstrained input minimization problem, and then solved by utilizing an improved conjugate gradient method. The total transition time is further minimized via one dimensional search. The almost superposition of Hammerstein systems (ASHS) is developed, and then exploited for precision control of hysteresis-Hammerstein systems. We showed that for Hammerstein operator satisfying a Lipschitz condition, a weak form of the ASHS---the linear combination of outputs approaches to the response to the linear combination of the corresponding inputs with a different set of combination coefficients---exists when there are enough output elements. The strict form of the ASHS---the coefficients of the output and the input combination match to each other exactly---holds for a certain choice of the inputs. The number of outputs in the ASHS is further quantified for hysteresis-Hammerstein system. We then present the realization of the ASHS for hysteresis-Hammerstein systems in the learning-based output tracking applications, based on the uniform B-splines for decomposition and the inverse Preisach modeling for superposition, where two optimizations of the ASHS for practical implementation are proposed. Moreover, for the trajectory decomposition problem arose in the ASHS, we further develop an asymptotic online trajectory decomposition (where the trajectory is only partially known at the decomposition instants) by only using one type of basis functions without truncation. The problem of trajectory approximation using only one basis function (along with its time-shifted copies) is addressed via a least-square minimization approach. The issue of truncating basis function at the boundaries is resolved via a zero-period extension (i.e., adding a zero-period to its beginning and end). It is shown that the coefficients of the basis functions at the initial portion of the extension period approach to zero as the length of the extension period increases. A sectional interactive decomposition algorithm is proposed for online trajectory decomposition through a trajectory redesign scheme.  Implementation of the frequency-domain iterative learning control (FD-ILC) in real-time for high-speed nanofabrication and AFM imaging becomes an issue as the FD-ILC involves multiple FFT/IFFTs that demand intensive online computation. An algorithm of optimal time-distributed fast Fourier transform and time-distributed inverse fast Fourier transform (OTD-FFT/TD-IFFT) is proposed to optimally distribute the FFT computation of a real-time sampled data sequence to minimize the per-sampling computational complexity without increasing the total computational complexity, and to obtain the entire Fourier transform sequence without latency. The proposed approach is extended to real-time IFFT computation, and then combined and applied to real-time FD-ILC implementation. The computational complexity analysis shows that the per-sampling computational complexity is substantially reduced by using the proposed approach.   The proposed optimal and learning-based output tracking and tracking-transition techniques can effectively achieve accurate high-speed nanofabrication. The effectiveness of the proposed techniques was demonstrated by simulation and experimental examples in accurate high-speed nanomanipulation utilizing an AFM probe driven by a piezoactuator. The optimal transition design and tracking approach was demonstrated by a simulation example in the control of the z-piezoactuator in an AFM system. It showed that the proposed approach can achieve minimal output oscillation and minimal input energy, and fast tracking under given input constraints. The proposed offline-learning based control technique was implemented to compensate for both hysteresis and dynamics in a piezoactuator system. It showed that high-speed, large-range precision tracking of hysteresis-dynamics systems, and considerable accuracy improvement when compared to PID control at different tracking speeds are achieved. A simulation example to decompose a trajectory sequentially online has demonstrated the effectiveness of the proposed online asymptotic trajectory decomposition technique. Finally, real-time implementation of FD-ILC based on an optimal time-distributed FFT was demonstrated through high-speed trajectory tracking on a piezoelectric actuator in experiments.