Environmental Engineering Reference
In-Depth Information
geometry, the Positivstellensatz, is used to estimate the domain of attraction for
the nonlinear system with the linear control law. The resulting region of attrac-
tion proves stability of the system over the desired portion of the state space.
Physically, this means that the linear control stabilizes the nonlinear system
over the desired operating range of LTC.
In [41, 43], the author and colleagues examined a natural next step, the
simultaneous control of peak pressure and combustion timing. The approach
outlined here approximately decouples the cycle-to-cycle dynamics of combus-
tion timing and peak in-cylinder pressure by controlling them on separate time
scales with different control inputs (inducted composition and effective com-
pression ratio, respectively). A physics-based H2 framework is used to deter-
mine a linear control law. Timing controller gains are selected via pole
placement to achieve a response time that is slightly slower than the pressure
controller.
An even more capable physics-based LTC control strategy [42, 50] outlines a
strategy for the simultaneous, coordinated control of combustion timing and
peak pressure on the same time scale through modulation of inducted gas
composition and effective compression ratio. The controller used is directly
synthesized from a linearized version of the complete control model outlined in
Section 4.3.3. Tracking responses for combustion timing and peak pressure
occur within 4-5 engine cycles. Additionally, a reduction in control effort is
realized due to the coordinated modulation of the control inputs.
4.3.5 Future Work Required for This LTC Control Approach
While the work completed to date is promising, it is important to note that these
results have been applied under the following limiting conditions and
assumptions:
- single-cylinder configuration: cylinder-to-cylinder dynamics have been
ignored at this point
- constant engine speed: engine speed will vary during practical implemen-
tation of LTC, must be considered
- molar ratio of reactants/products and effective compression ratio (both
modulated via intake and exhaust valve timing) have been the only con-
trol inputs considered: the cylinder-independent cycle-to-cycle injection
of fuel represents another capable control input which should be studied
using a physics-based approach
In order to practically implement LTC, the dynamics associated with cylin-
der-to-cylinder coupling and variable engine speed must be considered.
Furthermore, the availability of direct in-cylinder fuel injection provides the
opportunity to vary the amount of fuel delivered on a cycle-to-cycle and
cylinder-to-cylinder basis, a capability that has yet to be exploited in previous
