Marcel Sidi

Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances†

There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values. The plant is imbedded in a two-degree-of-freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries. Subject to the above, the design should be such as to minimize the effect of sensor white noise at the input to the plant. This report presents a design procedure for this purpose, based on frequency response concepts. The time-domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop-transmission function L(jω), in the form of continuous curves on the Nichols chart. Properties of L(jω) which satisfy these bounds with minimum effect of sensor white noise are derived. The design procedure is quite transparent, providing the designer with the insight to make necessary tradeoffs, at every step in the design process. The same design philosophy may be used to attenuate...There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values. The plant is imbedded in a two-degree-of-freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries. Subject to the above, the design should be such as to minimize the effect of sensor white noise at the input to the plant. This report presents a design procedure for this purpose, based on frequency response concepts. The time-domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop-transmission function L(jω), in the form of continuous curves on the Nichols chart. Properties of L(jω) which satisfy these bounds with minimum effect of sensor white noise are derived. The design procedure is quite transparent, providing the designer with the insight to make necessary tradeoffs, at every step in the design process. The same design philosophy may be used to attenuate...

Optimum synthesis of non-minimum phase feedback systems with plant uncertainty†

Linear time-invariant feedback systems in which the constrained plant transfer function has right half-plane zeros, are perforce non-minimum-phase, and their attainable benefits of feedback are inherently restricted. This paper presents criteria for determining whether a given set of performance specifications are achievable and, if so, a synthesis procedure is included for deriving the optimum design, defined as that with an effectively minimum loop transmission bandwidth. The properties of the optimum design are derived and its uniqueness proven, for both the minimum and non-minimum-phase feedback systems.

Brief paper: Feedback synthesis with plant ignorance, nonminimum-phase, and time-domain tolerances

This paper presents a design procedure for single-loop feedback systems in which the plant is nonminimum-phase, with ignorance in its parameters. The feedback system is to be designed such that the time response to a deterministic input lies within specified boundaries. Subject to the above, the design should be such as to minimize the effect of sensor noise at the input to the plant. The time domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop-transmission L(jw), in the form of continuous curves on the Nichols chart. However due to the nonminimum-phase nature of the plant, it may happen that no L(jw) can be found so that the design specifications of the problem are achieved, unless they are changed accordingly.

A combined QFT/H ∞ design technique for TDOF uncertain feedback systems

A new way of incorporating QFT principles into H X -control design techniques for solving the two-degrees of freedom feedback problem with highly uncertain plants is developed. The proposed practical design approach consists of two stages. In the first stage, the robustness problem, due to plant uncertainties, is solved by H X -norm optimization. In this stage, the controller inside the loop (the first degree of freedom) is designed, with the ultimate goal of minimizing the cost of feedback. Minimization of the sensor white noise amplification at the input to the plant is also performed using QFT principles. In the second stage of the design, the prefilter outside the loop (the second degree of freedom), is used to achieve the tracking specifications by conventional classical control theory, as practiced by the QFT design procedure. The combined QFT/H X design procedure for single input-single output (SISO) feedback systems is directly applicable to multi input-multi output (MIMO) feedback uncertain systems. The efficiency of the proposed technique is demonstrated with SISO and MIMO design examples for higly uncertain plants.

Synthesis of Feedback Systems with Large Plant Ignorance for Prescribed Time Domain Tolerances

Abstract There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values. The plant is imbedded in a two-degree-of-freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries. Subject to the above, the design should be such as to minimize the effect of sensor white noise at the input to the plant. This report presents a design procedure for this purpose, based on frequency response concepts. The time-domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop transmission function L(jω), in the form of continuous curves on the Nichols chart. Properties of L(jω) which satisfy these bounds with minimum effect of sensor white noise, are derived. The design procedure is quite transparent, providing the designer with the insight to make necessary trade-offs, at every step in the design process. The same design philosophy may be used to attenuate the effect of disturbances on plants with parameter ignorance.

Gain-bandwidth limitations of feedback systems with non-minimum-phase plants

The non-minimum-phase characteristics of physical plants strongly limit the openloop gain-bandwidth that can be achieved in output feedback control systems. Global limits due to NMP zeros and unstable poles on the achievable bandwidths are stated.

Synthesis of sampled feedback systems for prescribed time domain tolerance

This paper presents a design procedure for single-loop sampled feedback systems in which the plant transfer function has prescribed bounds on its parameters. The plant is imbedded in a ‘ two-degree-of-freedom system’, which is to be designed such that the system time response to a deterministic input lies within specified boundaries. The design procedure is based on frequency concepts. The time-domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop-transmission L(jv) [v =tang (π/WS)[, in the form of continuous curves on the Nichols chart. However, due to inherent theoretical difficulties existing in sampled feedback systems, it might happen that no L(jv) can be found so that the design specifications of the problem are achieved. The design procedure is transparent enough to guide the designer in which direction to change the specifications of the problem so that the next trial design will be successful.

Synthesis of linear time-varying non-minimum-phase systems with plant uncertainty†

The key element in a synthesis technique for uncertain linear time-varying systems, is the replacement of the linear time-varying plant set by an equivalent linear time-invariant plant set. Conditions under which the latter set must be so set up as to include non-minimum phase elements are presented. It is shown how to obtain the equivalent right half-plane zeros, which are sometimes accompanied by right half-plane poles. The synthesis technique previously usable only for uncertain ‘ minimum-phase ’ linear time-varying systems is extended to handle ‘ effectively non-minimum-phase ’ uncertain linear time-varying systems.

A Synthesis Theory for Nonlinear Systems with Plant Uncertainty

Abstract A nonlinear plant with parameter uncertainty is imbedded in a feedback system subjected to a finite set of inputs {x. (t)}. For each i there is a specified set of response tolerances. The synthesis procedure guarantees the response tolerances are satisfied over the range of uncertainty, for a large class of plants. The nonlinear plant is converted into an equivalent linear, time-invariant plant with parameter uncertainty, for which exact design is possible. Schauder’s fixed point theorem proves the equivalence is valid. The technique is applicable to any structure for which the equivalent linear, time-invariant problem is solvable.

A new approach for the design of multivariable feedback systems

A new design technique for multivariable feedback systems is presented. In this approach, n —1 open-loop transfer functions at different inputs of the plant, with all other feedback paths closed, are specified in advance, and are achieved exactly. The nth open-loop transfer function is a by-product of the design process, such that the overall feedback system is stabilized. The design approach is fitted to solve problems in which the plant elements can have non-stable poles and non-minimum phase zeros. The design process is straightforward, no iterations are necessary, and the achieved design copes exactly with the design specifications. The gainbandwidths of the different lis and the overall loop gain l* might be constrained due to non-stable poles and zeros of the plant elements. Based on the obtained different loop gains, any input output matrix T can bo achieved with the aid of an appropriate prefilter matrix F.