K. Havre

The use of RGA and condition number as robustness measures

Abstract The relative gain array (RGA) and condition number are commonly used tools in controllability analysis. In this paper we present new results that link these measures to control performance, measured in terms of the output sensitivity function with input and output uncertainty.

Achievable performance of multivariable systems with unstable zeros and poles

This paper examines the fundamental limitations imposed by unstable (right half plane; RHP) zeros and poles in multivariable feedback systems. We generalize previously known controller-independent lower bounds on the H

Selection of Variables for Regulatory Control Using Pole Vectors

Abstract This paper consider control structure design using the information given in the pole vectors. It is shown how the input and output pole vectors are related to the minimum input energy needed to stabilize a given unstable mode using one Single Input Single Output (Siso) control loop. The paper also look at stable but slow modes which need to be shifted further into the Left Half Plane (LHP) using feedback control. Moving stable slow modes are accomplished with pole placement and the results are interpreted in terms of Linear Quadratic Gaussian (LQG) control.

Effect of RHP zeros and poles on the sensitivity functions in multivariable systems

Abstract This paper examines the implications of Right Half Plane (RHP) zeros and poles on performance of multivariable feedback systems. The results quantify the fundamental limitations imposed by RHP-zeros and poles in terms of lower bounds on the peaks in the weighted sensitivity and complementary sensitivity functions.

Selection of variables for stabilizing control using pole vectors

For a linear multivariable plant, it is known from earlier work that the easy computable pole vectors provide useful information about in which input channel (actuator) a given mode is controllable and in which output channel (sensor) it is observable. In this note, we provide a rigorous theoretical basis for the use of pole vectors, by providing a link to previous results on performance limitations for unstable plants.

Control limitations for unstable plants

Abstract This paper discusses for linear systems the performance limitations imposed when the plant to be controlled is unstable (with RHP-poles). The first limitation is that the plant needs to stabilized using feedback control, and this requires the active use of manipulated inputs. The instability imposes a lower bound on the ℋ 2 - and ℋ ∞ -norms of the transfer function KS from outputs to inputs. Stabilization may thus be impossible if the input usage, due to measurement noise or disturbances, exceeds the saturation limits. These limitations are independent of the presence of RHP-zeros, but the combination of RHP-poles and RHP-zeros implies further performance deterioration. For a stabilized plant, the instability will manifest itself by the presence of a RHP-zero in the transfer function KS from the output to input used for control, which again imposes performance limitations in terms of the input movement.

Performance limitations for unstable SISO plants

This paper examines the fundamental limitations imposed by instability in the plant (right half plane, RHP, poles) on closed-loop performance. The main limitation is that instability requires active use of plant inputs, and we quantify this is terms of tight lower bounds on the input magnitudes required for disturbance and measurement noise rejection. These new bounds involve the H/sub /spl infin//-norm, which has direct engineering significance. The output performance in terms of disturbance rejection or reference tracking is only limited if the plant has RHP zeros. It is important to stress that the derived bounds are controller independent and that they are tight, meaning that there exists controllers which achieve the lower bounds.

Achievable H∞-performance of multivariable systems with unstable zeros and poles

Abstract This paper examines the limitations imposed by Right Half Plane (RHP) zeros and poles in multivariable feedback systems. The main result is to provide lower bounds on ‖WXV(s)‖∞ where X is S, SI, T or TI (sensitivity and complementary sensitivity). Previously derived lower bounds on the H∞-norm of S and T are thus generalized to the case with matrix-valued weights, including bounds for reference tracking, disturbance rejection, and input usage.