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A nonlinear multivariable feedback controller was defined for the idle to military operating regime (9 to 100 percent thrust) of the Pratt and Whitney Aircraft F401 variable cycle turbofan engine. The analytical design involved linearizing the F401 engine dynamics about five steady-state operating points between idle and military thrust, applying linear optimal control synthesis methods at each point, and combining the five optimal linear controllers into a single nonlinear controller which has feedback gains that are scheduled with high compressor speed. Variable fan, compressor and exhaust geometries as well as main burner fuel flow are coordinated by the controller to achieve rapid engine dynamic response., See also AD767425.

Synthesis procedures for nonlinear stochastic feedback control of gas turbine engines were developed and evaluated. Modern estimation and control procedures based upon separating the stochastic and deterministic aspects of the control problem were employed. The resulting closed-loop control consists of nonlinear deterministic feedback control logic designed using piecewise-linear/piecewise-optimal techniques, and an estimator designed using nonlinear filtering logic. Engine variables estimated from noise-corrupted measurements are fed back through the deterministic control logic to generate commanded inputs to the engine. Mode-switching logic was developed to provide smooth transition between small-signal regulation and large-signal transient modes of estimator/controller operation., See also Rept. no. UTRC-R77-942577-6 dated Mar 77, AD-A040 901.

Estimation algorithms for large-signal transient operation of nonlinear multivariable dynamic systems were developed and evaluated. Kalman methodology was employed in defining the filtering logic. Three estimation algorithms were defined based on representing the nonlinear system model by a reduced-order linear model, piecewise-linear model, and nonlinear model. Model-mismatch compensation techniques were established to account for the mismatch between the models in the filtering algorithms and the actual nonlinear system model. Filter gains for each algorithm were calculated off-line using modern state-space estimation techniques. An important constraint on the estimation algorithms is that their computational requirements be compatible with projected airborne digital computer capabilities. The estimation algorithms were evaluated and compared by application to noise-corrupted measurement data generated by a nonlinear digital dynamic F100/F401 engine simulation. Estimation of unmeasurable as well as measureable engine variables throughout the idle to military sea-level static operating regime (9 to 100 percent thrust) for large-signal transients was investigated. Measurable variables are available only through noisy sensors which contain inherent lags. On the basis of these noise-corrupted measurements, the filtering logic generates estimates of measurable and unmeasurable variables that are critical to satisfactory engine operation. Estimation of key engine variables from nominal-engine data, degraded-engine data and engine data with off-nominal noise statistics was evaluated.

Analytical procedures for a-priori assessment of key control variables in linear multi-input dynamic systems have been developed and evaluated. These procedures results in explicit, quantitative measures of control influence which allow a control designer to assess the relative importance of all control variables prior to actual feedback control design. In this manner the designer can select for dynamic modulation those controls which have the strongest influence on system dynamic response. The approach employed to develop key control assessment methodology is based on a modal interpretation of multivariable system dynamics. This approach is particularly well-suited here since mathematical expressions relating the coupling of each control variable into each mode of the system can be explicitly derived. These mathematical expressions provide important insight into the relationships among output variables, modes, control variables and the quadratic performance index used to generate linear multivariable feedback control. These relationships were used to define quantitative measures of relative control influence for both open-loop and closed-loop control situations.

Estimation and control algorithms were developed and evaluated for closed-loop regulation of noise-corrupted nonlinear multivariable dynamic systems. The stochastic regulation design procedures involve (1) deterministic multivariable feedback control design at a steady-state operating condition using linear quadratic regulator theory, (2) stochastic estimator design as defined in this study, and (3) closed-loop regulation based on feedback of estimated system state and selected output variables through the deterministic control logic. Four state estimation algorithms were defined: (1) digital smoothing of noisy measurements, (2) digital smoothing plus sensor compensation, (3) Kalman estimation logic using assumed linear plant and sensor dynamics, and (4) Kalman estimation with model-mismatch compensation logic which accommodates uncertainties associated with characterization of nonlinear plant dynamics by an assumed linear model. The developed methodology was evaluated by application to a nonlinear dynamic simulation of the F100/F401 turbofan engine at the military power operating condition.

Results directed toward the identification of multivariable gas turbine engine dynamics from stochastic input-output data are described. An identification algorithm based on modern state estimation theory was developed to identify the parameters of a linear time-invariant F100/F401 turbofan engine model. Unknown parameters of the F100/F401 model were introduced as auxiliary state variables thereby transforming the parameter identification problem to a nonlinear state estimation problem. The engine model was forced by commanded changes in main burner fuel flow and jet exhaust area. Gaussian noise was added to the commanded fuel flow to model metering valve uncertainties. Noise-corrupted measurements consisted of fan turbine inlet temperature, fan and compressor speeds, and main burner and afterburner pressures. The identification procedure was carried out at three steady-state design points between idle and military conditions.

An analytical synthesis method for the feedback control of nonlinear multivariable systems was developed. The synthesis procedure derived is based on linearizing a system about a set of closely-spaced steady-state operating points and applying linear optimization methods at each point. A single nonlinear control problem is thereby reduced to a series of linear control problems. This permits the use of established analytical and numerical methods associated with linear optimal control theory. At each operating point, an optimal linear feedback controller is generated by minizing a quadratic performance criterion. Weighting factors within each performance criterion enable the control designer to satisfy performance specifications by trading-off system response against control actuation rates. Nonlinear feedback control is then constructed by combining the series of linear controllers into a single nonlinear controller whose feedback gains vary with system state. (Modified author abstract)