HIGH-PERFORMANCE SPECTRAL METHODS FOR COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS

Recent research shows that by leveraging the key spectral properties of eigenvalues and eigenvectors of graph Laplacians, more efficient algorithms can be developed for tackling many graph-related computing tasks. In this dissertation, spectral methods are utilized for achieving faster algorithms in the applications of very-large-scale integration (VLSI) computer-aided design (CAD) First, a scalable algorithmic framework is proposed for effective-resistance preserving spectral reduction of large undirected graphs. The proposed method allows computing much smaller graphs while preserving the key spectral (structural) properties of the original graph. Our framework is built upon the following three key components: a spectrum-preserving node aggregation and reduction scheme, a spectral graph sparsification framework with iterative edge weight scaling, as well as effective-resistance preserving post-scaling and iterative solution refinement schemes. We show that the resultant spectrally-reduced graphs can robustly preserve the first few nontrivial eigenvalues and eigenvectors of the original graph Laplacian and thus allow for developing highly-scalable spectral graph partitioning and circuit simulation algorithms. Based on the framework of the spectral graph reduction, a Sparsified graph-theoretic Algebraic Multigrid (SAMG) is proposed for solving large Symmetric Diagonally Dominant (SDD) matrices. The proposed SAMG framework allows efficient construction of nearly-linear sized graph Laplacians for coarse-level problems while maintaining good spectral approximation during the AMG setup phase by leveraging a scalable spectral graph sparsification engine. Our experimental results show that the proposed method can offer more scalable performance than existing graph-theoretic AMG solvers for solving large SDD matrices in integrated circuit (IC) simulations, 3D-IC thermal analysis, image processing, finite element analysis as well as data mining and machine learning applications. Finally, the spectral methods are applied to power grid and thermal integrity verification applications. This dissertation introduces a vectorless power grid and thermal integrity verification framework that allows computing worst-case voltage drop or thermal profiles across the entire chip under a set of local and global workload (power density) constraints. To address the computational challenges introduced by the large 3D mesh-structured thermal grids, we apply the spectral graph reduction approach for highly-scalable vectorless thermal (or power grids) verification of large chip designs. The effectiveness and efficiency of our approach have been demonstrated through extensive experiments

An Active Disturbance Rejection Based Approach to Vibration Suppression in Two‐Inertia Systems

This study concerns the resonance problems found in motion control, typically described in a two‐inertia system model as compliance between the motor and the load. We reformulate the problem in the framework of active disturbance rejection control (ADRC), where the resonance is assumed to be unknown and treated as disturbance, estimated and mitigated. This allows the closed‐loop bandwidth to go well beyond the resonant frequency, which is quite difficult using existing methods. In addition, such level of performance is achieved with minimum complexity in the controller design and tuning: no parameter estimation or adaptive algorithm is needed, and the controller is tuned by adjusting one parameter, namely, the bandwidth of the control loop. It is also shown that the proposed solution applies to both the velocity and position control problems, and the fact that ADRC offers an effective and practical motion control solution, in the presence of unknown resonant frequency within the bandwidth of the control system. Finally, frequency response analysis is performed where stability margin is obtained before the simulation results are verified in the hardware experiments

Modified active disturbance rejection control for time-delay systems

Industrial processes are typically nonlinear, time-varying and uncertain, to which active disturbance rejection control (ADRC) has been shown to be an effective solution. The control design becomes even more challenging in the presence of time delay. In this paper, a novel modification of ADRC is proposed so that good disturbance rejection is achieved while maintaining system stability. The proposed design is shown to be more effective than the standard ADRC design for time-delay systems and is also a unified solution for stable, critical stable and unstable systems with time delay. Simulation and test results show the effectiveness and practicality of the proposed design. Linear matrix inequality (LMI) based stability analysis is provided as well