Use of State Feedback to Achieve a Nonovershooting Step Response for a Class of Nonminimum Phase Systems

52nd IEEE Conference on Decision and Control

Gao

2013

Section: Introductionmentioning

confidence: 99%

Nonovershooting multivariable tracking control for time-varying references

52nd IEEE Conference on Decision and Control

Gao

2013

“…In this paper we are concerned with the problem of designing an output feedback control law for (1) such that the output y of (1) tracks a step reference r ∈ R p with zero steady-state error with no overshoot. As such, we make the following standing assumption: Assumption 2.1: The system Σ is invertible, stabilizable, detectable and has no invariant zeros at the origin.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In [3] it is shown how to give two parameter feedback controller for an LTI plant that renders the step response nonovershooting. A common feature of these recent papers [1]- [3] was that they considered only SISO systems, which were assumed to be initially at rest. In some cases the transient response was deliberately slowed to avoid overshoot, which necessarily yielded a lengthy settling time.…”

Section: Introductionmentioning

confidence: 99%

“…For continuous time singleinput single-output (SISO) systems, in [1] an eigenstructure assignment method is given to obtain a non-overshooting LTI state feedback controller for plants with one non-minimum phase zero. Stable non-minimum phase SISO systems are considered in [2], where the existence of an output feedback controller is proved to give a non-overshooting step response, provided the plant has no zeros on the imaginary axis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Achieving a nonovershooting transient response with multivariable dynamic output feedback tracking controllers

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

2009

Abstract-We consider the use of dynamic output feedback control to improve the transient response to a step input, for invertible multivariable systems. A method is given for designing a linear time-invariant output feedback controller to asymptotically track a constant step reference with zero overshoot and arbitrarily small rise time, under some mild assumptions. I. INTRODUCTIONThe problem of designing control laws to ensure a linear time invariant (LTI) plant has desirable transient response to a step input has been studied for the past few decades. The primary performance objectives include achieving a small rise time while also minimising overshoot.Some recent papers have considered the problem of designing a suitable closed-loop feedback controller to achieve a non-overshooting response. For continuous time singleinput single-output (SISO) systems, in [1] an eigenstructure assignment method is given to obtain a non-overshooting LTI state feedback controller for plants with one non-minimum phase zero. Stable non-minimum phase SISO systems are considered in [2], where the existence of an output feedback controller is proved to give a non-overshooting step response, provided the plant has no zeros on the imaginary axis. In [3] it is shown how to give two parameter feedback controller for an LTI plant that renders the step response nonovershooting. A common feature of these recent papers [1]- [3] was that they considered only SISO systems, which were assumed to be initially at rest. In some cases the transient response was deliberately slowed to avoid overshoot, which necessarily yielded a lengthy settling time. In [4], the authors used a composite nonlinear (CNF) state-feedback controller consisting of a linear term chosen to yield a rapid response, and a nonlinear component designed to reduce overshoot. A smooth nonlinear error function is employed to tune the closed-loop dynamics. The authors showed their state feedback controller could also be implemented in conjunction with an observer scheme. However, their CNF scheme did not guarantee the step response will be non-overshooting.In our recent paper [6], the present authors considered invertible stabilisable MIMO systems, and used linear statefeedback control to design a non-overshooting controller for a step reference. The design methods proposed there make use of the combined eigenvalue and eigenvector placement

“…Corresponding conditions for discrete systems are given in [5]. A common feature of these recent papers [1]- [5] was that they considered only SISO systems, which were assumed to be initially at rest.…”

Section: Introductionmentioning

confidence: 99%

On the design of non-overshooting linear tracking controllers for right-invertible systems

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

2009

Abstract-We consider the use of linear state feedback control to achieve a non-overshooting step response, for rightinvertible non-square multivariable systems. A method is given for designing a linear time-invariant state-feedback controller to asymptotically track a constant step reference with zero overshoot and arbitrarily small rise time, under some mild assumptions. I. INTRODUCTIONThe problem of ensuring that a linear time invariant (LTI) plant has a non-overshooting step response has been studied for the past few decades. The problem is of importance in several applications such as manufacturing processes, where overshoot can compromise tolerances and damage the product.Some recent papers have considered the problem of designing a suitable closed-loop feedback controller to achieve a non-overshooting response. For continuous time singleinput single-output (SISO) systems, in [1] an eigenstructure assignment method is given to obtain a non-overshooting LTI state feedback controller for plants with one non-minimum phase zero. Stable non-minimum phase SISO systems are considered in [2], where the existence of an output feedback controller is proved to give a non-overshooting step response, provided the plant has no zeros on the imaginary axis. In [4] it is shown how to give two parameter feedback controller for an LTI plant that renders the step response non-overshooting. In [3] conditions are given for the existence of a controller to achieve a sign invariant impulse response, and hence also a non-overshooting step response. Corresponding conditions for discrete systems are given in [5]. A common feature of these recent papers [1]- [5] was that they considered only SISO systems, which were assumed to be initially at rest.Recently [9] considered invertible stabilisable multipleinput multiple-output (MIMO) systems, and used linear statefeedback control to design a non-overshooting controller for a step reference. The design methods proposed there make use of the combined eigenvalue and eigenvector placement methods given in [8], and are applicable to both continuous time and discrete time systems. Moreover, the design method is applicable to both minimum phase and non-minimum phase systems. Conditions are given under which a linear state-feedback controller can be obtained to asymptotically track a step reference with guaranteed zero overshoot, from