Morten Hovd

Simple frequency-dependent tools for control system analysis, structure selection and design: thr

Abstract The paper presents results on frequency-dependent tools for analysis, structure selection and design of control systems. This includes relationships between the relative gain array (RGA) and right half plane zeros, and the use of the RGA as a sensitivity measure with respect to individual element uncertainty and diagonal input uncertainty. It is also shown how frequency-dependent plots of the closely related performance relative gains (PRGA) and a new proposed disturbance measure, the closed-loop disturbance gains (CLDG), can be used to evaluate the achievable performance (controllability) of a plant under decentralized control. These controller-independent measures give constraints on the design of the individual loops, which when satisfied guarantee that the overall system satisfies performance objectives with respect to setpoint tracking and disturbance rejection.

Sequential design of decentralized controllers

Abstract A procedure for sequential design of decentralized controllers for linear systems is presented. It is shown how to include a simple estimate of the effect of closing subsequent loops into the design problem for the loop which is to be closed. In the examples the robust performance in terms of the structured singular value is used as the measure of control performance, but the procedure may be applied also for other performance measures.

Control of symmetrically interconnected plants

Abstract This paper is concerned with control of plants composed of n similar interacting subsystems. Such plants are common in practice and include paper machines, distribution networks, coating processes, and plants consisting of units operating in parallel. The transfer function matrices for these systems are block symmetric circulant. For H∞- and H2-optimal control, controller synthesis is simplified by considering n 2 + 1 independent problems of dimension n times smaller than the original problem. For the case of H∞-optimal control this also yields ‘super-optimality’, where the H∞ criterion is optimized in n directions, and not only in the worst direction. If the offdiagonal blocks (‘interactions’) are identical the matrix is termed block parallel, and controller synthesis involves only two independent subproblems of the same dimension as the subsystems. This leads to a dramatic reduction in dimension for systems composed of many subsystems.

Indirect Finite Control Set Model Predictive Control of Modular Multilevel Converters

The modular multilevel converter (MMC) is a potential candidate for medium/high-power applications, specifically for high-voltage direct current transmission systems. One of the main challenges in the control of an MMC is to eliminate/minimize the circulating currents while the capacitor voltages are maintained balanced. This paper proposes a control strategy for the MMC using finite control set model predictive control (FCS-MPC). A bilinear mathematical model of the MMC is derived and discretized to predict the states of the MMC one step ahead. Within each switching cycle, the best switching state of the MMC is selected based on evaluation and minimization of a defined cost function. The defined cost function is aimed at the elimination of the MMC circulating currents, regulating the arm voltages, and controlling the ac-side currents. To reduce the calculation burden of the MPC, the submodule (SM) capacitor voltage balancing controller based on the conventional sorting method is combined with the proposed FCS-MPC strategy. The proposed FCS-MPC strategy determines the number of inserted/bypassed SMs within each arm of the MMC while the sorting algorithm is used to keep the SM capacitor voltages balanced. Using this strategy, only the summation of SM capacitor voltages of each arm is required for control purposes, which simplifies the communication among the SMs and the central controller. This paper also introduces a modified switching strategy, which not only reduces the calculation burden of the FCS-MPC strategy even more, but also simplifies the SM capacitor voltage balancing algorithm. In addition, this strategy reduces the SM switching frequency and power losses by avoiding the unnecessary switching transitions. The performance of the proposed strategies for a 20-level MMC is evaluated based on the time-domain simulation studies.

SVD controllers for H 2 -, H ∞ - and m-optimal control0

Plant structure is utilized for the simplification of system analysis and controller synthesis. For plants where the directionality is independent of frequency, the singular-value decompositioin (SVD) is used to decouple the system into nominally independent subsystems of lower dimension. In H2− and H∞−optimal control, the controller synthesis can then be performed for each of these subsystems independently, and the resulting overall SVD controller will be optimal (the same will hold for any norm that is invariant under unitary transformations). In H∞−optimal control the resulting controller is also super-optimal, since a controller of dimension n × n will minimize the norm in n directions. For robust control in terms of the structured singular value μ, the SVD controller is optimal for a practically relevant class of block-diagonal structures and uncertainty and performance weights.

Implicit improved vertex control for uncertain, time-varying linear discrete-time systems with state and control constraints

The problem of regulating an uncertain and/or time-varying linear discrete-time system with state and control constraints to the origin is addressed. It is shown that feasibility and a robustly asymptotically stable closed loop can be achieved using an interpolation technique. The design method can be seen as an alternative to optimization-based control schemes such as Robust Model Predictive Control. Especially for problems requiring complex calculations to find the optimal solution, the present method can provide a straightforward suboptimal solution. A simulation demonstrates the performance of this class of constrained controllers.

A Procedure for Controllability Analysis

Abstract In this paper we give an overview of some of the tools available iorlinear controllability analysis. We present a procedure which may be described by the following main steps; 1. Generate model 2. Scale the plant 3. Compute controllability measures 4. Analyze controllability In the paper we raise issues in all of these categories. An FCC reactor is used as an example.

Robust output feedback model predictive control for linear systems via moving horizon estimation

This paper provides a simple approach to the problem of robust output feedback model predictive control (MPC) for linear systems with state and input constraints, subject to bounded state disturbances and output measurement errors. The problem of estimating the state is addressed by using moving horizon estimation (MHE). For such an MHE estimator, it is shown that the state estimation error converges and stays in some set, which is taken into account in the design of the output feedback MPC controllers. In the MPC formulation where the nominal system is considered, the constraints are tightened in a monotonic sequence such that satisfaction of the input and state constraints is guaranteed. Robust stability of an invariant set for the closed-loop original system is ensured. The performance of the approach is assessed via a numerical example.

Explicit constraint control based on interpolation techniques for time-varying and uncertain linear discrete-time systems

Abstract In this paper we consider the problem of regulating a time-varying and uncertain linear discrete-time system to the origin. It is shown how, by applying an interpolation technique and minimizing an appropriate objective function, one can achieve feasibility and a robustly and asymptotically stable closed-loop behavior. Moreover, we show that the control is a piecewise affine and continuous function of state. A simulation result demonstrates the performance of our approach.

Inverse parametric convex programming problems via convex liftings

Abstract The present paper introduces a procedure to recover an inverse parametric linear or quadratic programming problem from a given polyhedral partition over which a continuous piecewise affine function is defined. The solution to the resulting parametric linear problem is exactly the initial piecewise affine function over the given original parameter space partition. We provide sufficient conditions for the existence of solutions for such inverse problems. Furthermore, the constructive procedure proposed here requires at most one supplementary variable in the vector of optimization arguments. The principle of this method builds upon an inverse map to the orthogonal projection, known as a convex lifting. Finally, we show that the theoretical results has a practical interest in Model Predictive Control (MPC) design. It is shown that any linear Model Predictive Controller can be obtained through a reformulated MPC problem with control horizon equal to two prediction steps.