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2) and the time-varying wall-wetting dynamics. In particular, we want to guarantee the stability of the closed-loop system and also minimize the effect of the disturbances for any conceivable wall-wetting dynamics variations. The proposed control architecture is illustrated in Fig. 5. This scheme has five possible components, that is a feedback controller K (Θ), a feed-forward controller K f (Θ), a filter L(q), an integrator I (q), and possibly a differentiator D(q) (if a PID controller is desired).
The parameter variation of Ne is represented by γ as shown in Eq. 10). The upper LFTs (see Appendix A) inside the dotted box in Fig. 7, M 1 and M βα are used to isolate the time-varying β parameters βδ (k) and αδ (k) . 20) ⎤ ⎥ ⎦. 21) 54 4 Gain-Scheduling Control of Port-Fuel-Injection Processes βδ β0 w1 αδ u − α0 − 1 m0a q− 1 cq− 1 y βδ M1 β Δ q− 1 − Mα β 1 c − w3 γ I9 − z ys O2 Sensor w2 Fig. 22) ⎤ ⎥ βδ (k) 0 . 3 LPV Gain-Scheduling Controller Design 55 where x(k) ∈ Rn is the state at time k, w(k) ˜ ∈ Rr is the unweighted exogenous input, p z(k) ∈ R is the error output, p(k), l(k) ∈ Rn p are the pseudo-input and pseudooutput connected by Θ(k), and u(k) ∈ Rm is the control input.
Furthermore, the control synthesis method used in  relies on gridding the parameter space at a finite number of grid points. In , a large variable time delay is present in the A/F ratio control loop for a lean burn spark ignition engine. LPV control methods are used to compensate for the variable time delay. In , a discrete-time, LPV model is developed with manifold absolute pressure, exhaust valve closing, and inlet valve opening as the time-varying parameters. However, only manifold absolute pressure is used as a scheduling parameter in the gain-scheduling control that is synthesized.