Maximally robust controllers for multivariable systems

Published versio

On the gap between the complex structured singular value and its convex upper bound

Published versio

A STATE-SPACE ALGORITHM FOR THE SOLUTION OF THE 2-BLOCK SUPEROPTIMAL DISTANCE PROBLEM

Published versio

An explicit state-space approach to the one-block super-optimal distance problem

An explicit state-space approach is presented for solving the super-optimal Nehari-extension problem. The approach is based on the all-pass dilation technique developed in (Jaimoukha and Limebeer in SIAM J Control Optim 31(5):1115–1134, 1993) which offers considerable advantages compared to traditional methods relying on a diagonalisation procedure via a Schmidt pair of the Hankel operator associated with the problem. As a result, all derivations presented in this work rely only on simple linear-algebraic arguments. Further, when the simple structure of the one-block problem is taken into account, this approach leads to a detailed and complete state-space analysis which clearly illustrates the structure of the optimal solution and allows for the removal of all technical assumptions (minimality, multiplicity of largest Hankel singular value, positive-definiteness of the solutions of certain Riccati equations) made in previous work (Halikias et al. in SIAM J Control Optim 31(4):960–982, 1993; Limebeer et al. in Int J Control 50(6):2431–2466, 1989). The advantages of the approach are illustrated with a numerical example. Finally, the paper presents a short survey of super-optimization, the various techniques developed for its solution and some of its applications in the area of modern robust control

Feedforward PID control of full-car with parallel active link suspension for improved chassis attitude stabilization

PID control is commonly utilized in an active suspension system to achieve desirable chassis attitude, where, due to delays, feedback information has much difficulty regulating the roll and pitch behavior, and stabilizing the chassis attitude, which may result in roll over when the vehicle steers at a large longitudinal velocity. To address the problem of the feedback delays in chassis attitude stabilization, in this paper, a feedforward control strategy is proposed to combine with a previously developed PID control scheme in the recently introduced Parallel Active Link Suspension (PALS). Numerical simulations with a nonlinear multi-body vehicle model are performed, where a set of ISO driving maneuvers are tested. Results demonstrate the feedforward-based control scheme has improved suspension performance as compared to the conventional PID control, with faster speed of response in brakein a turn and step steer maneuvers, and surviving the fishhook maneuver (although displaying two-wheel lift-off) with 50 mph maneuver entrance speed at which conventional PID control rolls over

Simultaneous stabilisation approach for power system damping control design through TCPAR employing global signals

A robust damping control design methodology for a thyristor controlled phase angle regulator using global signals is proposed based on the simultaneous stabilisation approach. The numerical design algorithm determines the controller parameters in order to guarantee closed-loop poles in the left half plane with preferential treatment to those corresponding to the inter-area modes. Plant models under different operating conditions are incorporated in the design formulation to achieve the desired performance robustness. A three-input/single-output controller is designed for the TCPAR to provide adequate damping to the critical inter-area modes of a study system model. Based on the observability of the inter-area modes, real power flows from remote locations are used as feedback stabilising signals. The damping performance of the controller is examined in the frequency and time domains and is found to be robust against varying power-flow patterns, nature of loads, tie-line strengths and system non-linearities, including saturation

Modeling and control of TCV

A new approach to the modeling and control of tokamak fusion reactors is presented. A nonlinear model is derived using the classical arguments of Hamiltonian mechanics and a low-order linear model is derived from it. The modeling process used here addresses flux and energy conservation issues explicitly and self-consistently. The model is of particular value, because it shows the relationship between the initial modeling assumptions and the resulting predictions. The mechanisms behind the creation of uncontrollable modes in tokamak models are discussed. A normalized coprime factorization H-infinity controller is developed for the the Tokamak A Configuration Variable (TCV), CRPP-EPFL, Lausanne, Switzerland, tokamak using the linearized model, which has been extensively verified on the TCV and JT-60U, JAERI, Naka, Japan, tokamaks. Recent theory is applied to reduce the controller order significantly whilst guaranteeing a priori bounds on the robust stability and performance. The controller is shown to track successfully reference signals that dictate the plasma's shape, position and current. The tests used to verify this were carried out on linear and nonlinear models

Model predictive control based on mixed ℋ2/ℋ∞control approach for active vibration control of railway vehicles

This paper investigates the application of model predictive control technology based on mixed H2/H-inf control approach for active suspension control of a railway vehicle, the aim being to improve the ride quality of the railway vehicle. Comparisons are made with more conventional control approaches, and the applicability of the linear matrix inequality approach is illustrated via the railway vehicle exampl

Metalearning-Based Alternating Minimization Algorithm for Nonconvex Optimization

In this article, we propose a novel solution for nonconvex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of subproblems corresponding to each variable and then iteratively optimizes each subproblem using a fixed updating rule. However, due to the intrinsic nonconvexity of the original optimization problem, the optimization can be trapped into a spurious local minimum even when each subproblem can be optimally solved at each iteration. Meanwhile, learning-based approaches, such as deep unfolding algorithms, have gained popularity for nonconvex optimization; however, they are highly limited by the availability of labeled data and insufficient explainability. To tackle these issues, we propose a meta-learning based alternating minimization (MLAM) method that aims to minimize a part of the global losses over iterations instead of carrying minimization on each subproblem, and it tends to learn an adaptive strategy to replace the handcrafted counterpart resulting in advance on superior performance. The proposed MLAM maintains the original algorithmic principle, providing certain interpretability. We evaluate the proposed method on two representative problems, namely, bilinear inverse problem: matrix completion and nonlinear problem: Gaussian mixture models. The experimental results validate the proposed approach outperforms AM-based methods

VERTICAL STABILIZATION OF TOKAMAK PLASMAS

The design of a controller which will control the current in the active control coils of a tokamak fusion reactor is discussed. At this stage, the task is to stabilize and control the vertical position of the plasma. As the linearized models of the plasma dynamics are of very high order, any control system design work must be preceded by a model reduction phase. Model reduction methods based on truncated balancing are used. The control systems are designed using H∞-based methods. The initial study described indicates that the infinite element models which describe the plasma's vertical dynamics are essential low order. The Krylov subspace method of finding approximate solutions to the gramian equations worked well in this application, and the subsequent model reduction steps were computationally manageable. The H∞ method for designing controllers worked well, and the closed-loop performance seems relatively insensitive to changes of operating point