Strong stabilization of MIMO systems with restricted zeros in the unstable region

The strong stabilization problem (i.e., stabilization by a stable feedback controller) is considered for a class of finite dimensional linear, time-invariant, multi-input multioutput plants. It is assumed that the plant satisfies the parity interlacing property, which is a necessary condition for the existence of strongly stabilizing controllers. Furthermore, the plant class under consideration has no restrictions on the poles, on the zeros in the open left-half complex plane, on the zeros at the origin or at infinity; but only one finite positive real zero is allowed. A systematic strongly stabilizing controller design procedure is proposed that applies to any plant in the class, whereas alternative approaches may work for larger class of plants but only under certain sufficient conditions. The freedom available in the design parameters may be used for additional performance objectives although the only goal here is strong stabilization. In the special case of single-input single-output plants in the class considered, the proposed stable controllers have order one less than the order of the plant. © 2008 IEEE

Low order controller design for systems with time delays

Finite-dimensional controller synthesis methods are developed for some classes of linear, time-invariant, single-input single-output, or multi-input multi-output systems, which are subject to time delays. The proposed synthesis procedures give low-order stabilizing controllers that also achieve integral-action so that constant reference inputs are tracked asymptotically with zero steady-state error. © 2011 IEEE

Integral action controllers for systems with time delays

Consider a stabilizing controller C 1 for a given plant P. If C 1 and P do not have any zeros at the origin, then one can use a cascade connected PI (proportional plus integral) controller C pi with C 1 and keep the feedback system stable. In this work we examine the allowable range of the integral action gain in C pi , and discuss how C 1 should be chosen to maximize this range for systems with time delays. © 2009 Springer-Verlag Berlin Heidelberg

Robust controller design based on reduced order plants

Two dual controller design methods are proposed for linear, time-invariant, multi-input multi-output systems, where designs based on a reduced order plant robustly stabilizer higher order plants with additional poles or zeros in the stable region. The additional poles (or zeros) are considered as multiplicative perturbations of the reduced plant. The methods are tailored towards closed-loop stability and performance and they yield estimates for the stability robustness and performance of the final design. They can be considered as formalizations of two classical heuristic model reduction techniques. One method neglects a plant-pole sufficiently far to the left of dominant poles and the other cancels a sufficiently small stable plant-zero with a pole at the origin

Reliable decentralised control of delayed MIMO plants

Reliable decentralised proportional-integral-derivative controller synthesis methods are presented for closed-loop stabilisation of linear time-invariant plants with two multi-input, multi-output (MIMO) channels subject to time delays. The finite-dimensional part of plants in the classes considered here are either stable or they have at most two poles in the unstable region. Closed-loop stability is maintained with only one of the two controllers when the other controller is turned off and taken out of service. © 2010 Taylor & Francis

PI and low-order controllers for two-channel decentralized systems

A systematic design method is proposed for simple loworder decentralized controllers in the cascaded form of proportional-integral and first-order blocks. The plant is linear, time-invariant and has two channels, each with a single-input and single-output; there may be any number of poles in the region of stability, but the unstable poles can only occur at the origin

Resilient PI and PD controllers for a class of unstable MIMO plants with I/O delays

Recently (Gündeş et al., 2006) obtained stabilizing PID controllers for a class of MIMO unstable plants with time delays in the input and output channels (I/O delays). Using this approach, for plants with one unstable pole, we investigate resilient PI and PD controllers. Specifically, for PD controllers, optimal derivative action gain is determined to maximize a lower bound of the largest allowable controller gain. For PI controllers, optimal proportional gain is determined to maximize a lower bound of the largest allowable integral action gain. Copyright © 2006 IFAC

Plant Order Reduction for Controller Design

Two dual methods of plant order reduction for controller design are proposed for linear, time-invariant, multi-input multi-output systems. The model reduction methods are tailored towards closed-loop stability and performance and they yield estimates for the stability robustness and performance of the final design. They can be considered as formalizations of two classical heuristic model reduction techniques: One method neglects a plant-pole sufficiently far to the left of dominant poles and the other cancels a sufficiently small stable plant-zero with a pole at the origin

Stable ℋ∞controller design for systems with time delays

One of the difficult problems of robust control theory is to find strongly stabilizing controllers (i.e. stable controllers leading to stable feedback system) which satisfy a certain ℋ∞ performance objective. In this work we discuss stable ℋ∞controller design methods for various classes of systems with time delays. We consider sensitivity minimization problem in this setting for SISO plants. We also discuss a suboptimal design method for stable ℋ∞controllers for MIMO plants. © 2010 Springer-Verlag Berlin Heidelberg

Strong stabilization of a class of MIMO systems

Stabilization of finite dimensional linear, time-invariant, multi-input multi-output plants by stable feedback controllers, known as the strong stabilization problem, is considered for a class of plants with restrictions on the zeros in the right-half complex plane. The plant class under consideration has no restrictions on the poles, or on the zeros in the open left-half complex plane, or on the zeros at the origin or at infinity; but only one finite positive real zero is allowed. A systematic strongly stabilizing controller design procedure is proposed. The freedom available in the design parameters may be used for additional performance objectives although the only goal here is strong stabilization. In the special case of single-input single-output plants within the class considered, the proposed stable controllers have order one less than the order of the plant. © 2006 IEEE