In order to meet stringent emission requirements, it is becoming ever more important that combustors are designed to operate in a lean premixed mode. Although this operation reduces the NOx emissions, it has the disadvantage that premixed flames are particularly susceptible to self-excited oscillations. These oscillations create large-scale pressure waves which can cause structural damage to the combustion system. These self-excited combustion oscillations result from an interaction between unsteady combustion and acoustic waves : unsteady combustion generates sound, while acoustic waves reflected from the boundaries of the combustor perturb the combustion still further.

This problem is currently being experienced by all manufacturers of industrial gas turbines and is leading to long and costly development and commissioning times. The next generation of aero engine combustors are also required to have low NOx levels and damaging self-excited oscillations are also being experienced on development engines.

Passive dampers are currently used within the industry but they require substantial tuning and have a limited operational range over which they can ensure system stability.

An alternative solution is to use active control which provides a way of extending the stable operating range of a combustion system. The most practical control actuator injects unsteadily some fuel (in practice the mean fuel supply is modulated) in order to modify the unsteady heat release and hence break the damaging coupling between unsteady heat release and acoustic waves. To know how much fuel needs to be injected to control the instabilities, a

signal D, which is usually but not always a pressure signal, is measured at a reference location and is sent to the controller, which in turn produces a voltage V driving the injection system.

Many different active systems have been employed to control such combustion systems but they have all suffered from the inherent problem that time delays occur within the combustor between the control signal V and the detected signal D. Presently, the only method which can ensure that there will be no time delay is to measure D at the flame, which requires high temperature instrumentation, and to inject the fuel-air mix directly into the flame in the combustion zone which is obviously a very dangerous procedure.

Time delays can be caused by a number of factors. If fuel alone is injected into the flame, there will be a time delay while it mixes with sufficient air for combustion to occur. Further, if the fuel-air mix is injected upstream of the combustion zone, there will be a convection time delay before the fuel reaches the combustion zone. Yet a further time delay occurs between a change in the conditions in the combustion zone and that change being detected by the detection apparatus, thus called a detection time delay. In total, these time delays can adversely affect the accuracy of the controller and hence the stability of a combustion system.

However, to be useful in practice, an active controller needs to be effective across a range of operating conditions. An efficient approach is to use an adaptive controller in which the controller parameters are continually updated as the engine condition changes.

Thus the present invention relates, in particular, to controllers which can compensate for such time delays and reliably update the controller parameters to accommodate changes in combustor operating conditions.

There are already some algorithms that describe how to update the controller parameters, but so far they are

either based on a specific model or they provide no guarantees that the controller can stabilise the self- excited combustion process.

The most popular adaptive scheme used for active control of combustion instability is the Least Mean Squares (LMS) algorithm applied to an IIR (Infinite Impulse Response) filter. The LMS is very attractive because it does not require any model as the combustion process is considered as a"black box"and is learnt during a system identification procedure which can be performed either off- line or on-line. However, the major drawback is that an LMS controller might lead to a divergence of the control scheme if, for some operating conditions, the poles of the IIR become unstable. The features of an LMS controller have been extensively studied and it was found that it was necessary to introduce a parallel algorithm (based on the Laguerre's method) to prevent a starting divergence due to the controller.

Other adaptive schemes already developed include a system employing neural networks, which is a nonlinear version of the LMS controller, and a minimisation scheme based on the downhill simplex algorithm.

However, none of these schemes provide a guarantee that the controller can stabilise the self-excited combustion process and they do not account for the time delays within the system.

An efficient way to prevent any divergence of the adaptive control scheme is to use systematic methods for designing stable adaptive systems. An adaptive controller, called STR (Self-Tuning Regulator), is already known and is based on a Lyapunov stability analysis and is therefore guaranteed to be stable for any operating conditions.

Furthermore, the STR has the advantage of avoiding a system identification procedure (which is one of the main

difficulties when trying to implement a LMS controller) since it will use little information about the physical process. However, so far, the STR has only been designed with respect to a specific model, and does not have general application. Furthermore, the STR does not account for time delays in the combustion system.

Rather than provide a solution for a particular premixed combustor, the present invention aims to determine the general features of a self-excited combustion system, and then to exploit them to design an adaptive active controller that is guaranteed to stabilise the combustion system. Hence, the present invention is also intended to provide control for a wide range of combustion systems.

A further aim of the present invention is to guarantee stabilisation in the presence of time delay in the combustion system.

According to the present invention, there is provided a controller for controlling self excited oscillations in a combustion system, the controller comprising : a phase lead compensator ; and a Smith controller ; wherein the controller has the form : wherein V is the output voltage from the controller which will be used to drive the actuator, D is the input signal to the controller used to detect conditions in the combustor, S is a data vector of length N+2, K is the

control parameter vector of length N+2, F is a filtered version of S, Vz is a filtered version of V, a and Zc are positive constants, i is the time delay between V and D, dt is the logging period and N=i/dt.

More precisely, (k1lk2lzc) define the phase-lead compensator, where kl is a positive gain, k2 and Zc are positive constants such that the compensator increases the phase of a signal passing in a frequency range (Zcl Zc+ k2)- The Smith controller is a summation means on past values of V, the weighting coefficients of the sum being denoted as Si, i=l, 2,... N.

This is a new use of a Smith controller as typically it is used with a high order filter (i. e. the order of the plant) whose coefficients are chosen by pole placement ideas to give the required closed-loop characteristics.

However, this is impractical in the present system which, because of time delays, is essentially of infinite order and thus the required filter would be of infinite order.

Instead, we combine the Smith controller with a phase-lead compensator and use root-locus ideas to show that the control parameters of the system can be chosen so that the closed-loop system is stable. This is a surprising outcome as the prior art devices all teach away from this approach.

The value of the control parameter K achieving control depends on the combustion system characteristics and on the combustor operating conditions. Therefore, in order to have a controller independent of a detailed description of the combustion system and to have an optimised control response under varying operating conditions, it is more adequate to determine the value of K adaptively. An adaptive rule for K, derived from a Lyapunov stability analysis and hence guaranteed to lead to stabilising the value of K, follows :

The controller may be used with any combustion system but preferably with lean mixed premixed prevapourised combustors and aero engine afterburners.

Preferably the controller can function when the total time delay is as much as three cycles of pressure oscillation.

An embodiment of the present invention will now be described with reference to the accompanying drawings, in which : Fig. 1 is a schematic representation of a combustion system ; Fig. 2 shows a schematic representation of a fixed low order controller structure for a combustion system with a known time delay T ; Fig. 3 shows a schematic representation of a low order adaptive controller for use in a combustion system with a known time delay ; and Fig. 4 is a block diagram of an unstable combustor with saturated amplitude control signal.

A wide class of combustion systems, including lean premixed prevapourised (LPP) combustors and aero engine afterburners, can be modelled as a combustion section 1 embedded within a network of pipes, as shown in Fig. 1.

An actuator 2 can inject a disturbance to the combustion zone 3 during active control. Fig. 1 shows, in solid line, the open loop arrangement of a self-excited combustion process and, in dotted line, a possible closed- loop control arrangement 4.

The flow at the inlet to the combustor is assumed to be isentropic. Moreover, as the frequency of the oscillations of interest are low, the combustion zone is

short compared with the wavelength. Further, since acoustic energy is only transported by plane waves, it is sufficient to consider one dimensional disturbances. It is possible to model the pressure, velocity and density both upstream and downstream of the flame as linear combinations of waves. The boundary conditions of the model can be set such that it is possible to neglect the conversion of combustion generated entropy waves into sound at any downstream nozzle and this is good approximation when the time taken for entropy waves to convect through the straight duct exceeds their diffusion time. It then follows that, for a general class of boundary conditions, the amplitude of the reflected pressure waves is strictly less than the incoming wave. This is the case for a choked end, an open end with appropriate loss mechanisms, and for a network of pipes.

In the Laplace domain, the generation of an unsteady velocity ul (t) at the flame due to the unsteady heat release Q (t) can be described by the transfer function The combustion response can be described by a further transfer function In many circumstances, H (s) would include substantial time delays. Many different models for the flame transfer function H (s) are known but, as the present invention is directed to general combustion systems rather than specific designs, some general, non-restrictive observations about the structure of H (s) can be made.

Firstly, the flame is stable when there is no driving velocity ul, which means that the poles of H (s) are stable.

Secondly, the flame response has a limited bandwidth and therefore H tends to zero when s tends to infinity.

These assumptions fit many different flame models and the eigenfrequencies can be determined such that they satisfy 1-G (s) H (s) = 0 When a combustor is unstable, the roots of this equations have a real part which is greater than zero, indicating that the disturbances grow exponentially in time.

In order to apply active control to a self-excited combustion system, an actuator is used to inject a disturbance and hence break the damaging coupling between unsteady combustion waves and acoustic waves. The two most commonly used active control inputs are loudspeaker forcing and fuel forcing. The more important of these is fuel forcing as this is the most relevant for practical applications. In this case, an actuator is driven to provide extra fuel (and sometimes air) which in turn produces additional heat release. In order to stabilise such a self-excited combustion system, it is necessary to characterise the transfer function which is a ratio of the fluctuating detection signal D measured at a location Xref to a voltage V, which is a voltage sent to the actuator.

The external voltage V results in additional heat release Qc which is described by the following transfer function, where Wa (s) represents the actuator dynamics.

Typically, the actuator 2 is a valve having the characteristics of a mass-spring-damper system, whose dynamics are described by the transfer function Wa (s). If the fuel-air mixture is injected directly into the combustion zone, the combustion response will be instantaneous, i. e. the time delay will be zero. However, if only fuel is added, there will be a small mixing time delay before it is burnt. As it is hazardous to inject fuel directly into the flame, it is usual to introduce the additional fuel from a distance upstream of the combustion zone and this leads to a convection time delay between injection and combustion. The sum of mixing and convection time delays is described by Ta.

The open loop transfer function of the combustion system with this actuator be written in the form where Wo (s) is a combination of G (s), H (s) and Wa (s) and is infinite dimensional, and T tdet + ta T is the total time delay in the system between signal D and the voltage V, Ta is the actuation time delay and Tdet is the detection time delay.

Since the actuator has limited bandwidth, we can approximate the open-loop transfer function in a finite dimensional form

where ko is a constant, Zo and Ro are two coprime and monic polynomials and i is a known time delay. Three general open-loop properties can be derived : Zo (s) has only stable zeroes, the difference between the degree of Ro and the degree of Zo is 1 or 2, and the gain ko is positive. The presence of such a time delay makes previous controllers inadequate especially as it is of the order of the period of the unstable mode. While control of systems in the presence of time delay is well known, such control has not yet suitably been achieved.

In a combustion system having a known time delay, Fig.

2 represents a suitable fixed controller structure. The combustion section 1 is coupled to a closed loop controller 4 having a Smith controller 5. The Smith controller 5 and the two feedback loops 6, 7 have fixed parameters.

One known method to deal with time delays is to use a Smith controller which attempts to estimate the feature output of the system using a known model and provides an appropriate stabilisation action. Further, it is known to modify Smith controllers to control systems which are open loop unstable by using finite-time integrals of inputs V to estimate the future outputs.

In this way, we implement a Smith controller using a finite time integral given by where A (o) is a weighting function.

In practice, this finite-time integral due to the Smith controller is represented by

where N=l/dt and dt is the logging period.

From the three open-loop properties of the system, it can be shown that the Smith controller 5, in association with a first order compensator represented by the feedback loops 6, 7, is guaranteed to stabilise the combustion process. In other words, the weighting coefficients Xi, #2,..., #N in the Smith controller and the controller coefficients kl and k2 in the feedback loops 6, 7 can be chosen such that the closed-loop system is stable.

The arrangement of Fig. 3 provides a similar controller structure to that of Fig. 2 but, in this case, <BR> <BR> <BR> the Smith controller 5'and the two feedback loops 6l, 7' have adaptive parameters, that is the parameters are variable dependent upon the conditions within the combustor section 1.

For the closed-loop configurations of Figs. 2 and 3, the control parameter vector K and data vector S are defined by <BR> <BR> <BR> <BR> and K (t) A, (t) IT<BR> and S (t) = [D(t),Vz(t),V(t-Ndt),V(t-(N-1)dt),...,V(t-dt)]T where Vz is a filtered version of V defined as follows : ###(t)+zcVz(t)=V(t) Further, we define a filtered version F of the data vector S as dF (t)+aF(t)=S(t)<BR> dt where a and Zc are positive constants.

The stability of the closed-loop system in Figs. 2 and 3 is guaranteed when the controller output is defined by

For the fixed controller defined in Fig. 2, the control parameter K is fixed and its value depends on the conditions within the combustor section 1.

However, control across a range of operating conditions may be obtained by using the adaptive controller given in Fig. 3. Then, provided the following adaptive rule for the control parameter K is used ) =-D (-.) the control parameter K is guaranteed by Lyapunov stability analysis to converge to a stabilising value for K.

Figure 4 shows a system in which control voltage V has saturated and the previous control system has, for modelling purposes, a saturation block inserted therein to factor in the effects of saturation.

In many situations the control voltage for the fuel injection system will become saturated under certain conditions. It will be appreciated that this introduces a non linearity into the control that, in such circumstances, needs to be handled by the controller. A controller according to the invention can, however, be modified in order to take into account amplitude saturation on the control voltage V. Essentially, in the presence of saturation, the unsaturated control signal, denoted is still obtained, using equation : However, the actual signal sent to the fuel injection system is the saturated signal V, which is defined as follows :

coefficient is a leakage This adaptive rule is guaranteed to stabilise the combustion system for #F# and ||K|| initially bounded. These initial conditions on IIFII and Kj) are satisfied in a practical combustor when control is switched on while the pressure limit cycle is already established, and with the control parameter K set to zero initially.

Further, the stability domain is reduced when the amplitude constraint become higher (ie when is reduced). These qualitative results make sense as successful control cannot be expected when the amplitude of the control signal becomes too small in comparison with the amplitude of the oscillations to be damped.