Techniques are previously known for improving fuel consumption in spark ignition engines by performing combustion under lean air/fuel ratio conditions, in which the air/fuel ratio of the mixture in the cylinders is larger than the stoichiometric air/fuel ratio (or theoretical air/fuel ration).  For example, as illustrated in Laid-open Japanese Patent Application No.  H. 10-274085, a technique is known in which an injection valve that injects fuel directly into the combustion chamber is provided and super-lean combustion is produced by conducting stratified charge combustion in the low rotational speed low load region etc.  Specifically, such stratified charge combustion consists in altering the composition ratio of the mixture in the vicinity of the spark plug in the ignition period by injecting fuel in the compression stroke, while controlling the rate of air intake and rate of fuel injection such as to produce a condition in the combustion chamber as a whole that is much leaner than the stoichiometric air/fuel ratio, and performing combustion with forced ignition by the spark plug in this condition. 
When super-lean combustion is performed by stratified charge combustion as described above, thermal efficiency is improved and the air intake rate becomes large, reducing the intake negative pressure and thereby greatly improving fuel consumption.  Also, in such a super-lean stratified charge combustion condition, even if some of the air that is present in excess is replaced by EGR, fully satisfactory combustion is still achieved, so a comparatively large amount of EGR may be employed and this is thereby beneficial in lowering NOx etc.  Thus, even though this large amount of EGR is introduced, the benefit of a lowered pumping loss is still obtained and thermal efficiency is also increased compared with ordinary combustion in which the air intake rate and EGR rate are controlled without layering; the benefit of improved fuel consumption is thereby obtained. 
However, when stratified charge combustion is performed, although, as the air/fuel ratio is made leaner, improved fuel consumption is obtained up to a certain point, if the mixture becomes leaner than a certain degree, the combustion rate becomes too low, with the result that the combustion occurring in the vicinity of the final period does not contribute to work, so, contrariwise, fuel consumption tends to deteriorate.  Thus, there were limits to the extent to which fuel consumption improvement could be achieved by increasing leanness in stratified charge combustion. 
Compression ignition has been studied as another technique for improving fuel consumption.  This compression ignition consists in self-ignition of fuel at high temperature and high pressure in a combustion chamber in the latter period of the compression stroke, in the same way as in the case of a diesel engine.  If such compression ignition is performed, even under conditions of a super-lean air/fuel ratio or conditions of introduction of a large amount of EGR, combustion occurs at once throughout the entire combustion chamber.  Slow combustion, which does not contribute to work, is thereby avoided, which is beneficial in improving fuel consumption. 
However, in an ordinary spark ignition engine (gasoline engine), forced ignition for combustion is necessary and the temperature and pressure within the combustion chamber in the vicinity of the top dead center in compression are not elevated to a sufficient degree to produce compression ignition; thus special expedients must be adopted if the temperature or pressure in the combustion chamber is to be raised to the considerable degree necessary to achieve compression ignition.  However, in a conventional spark ignition engine, it is difficult to raise the temperature or pressure in the combustion chamber to such an extent as to produce compression ignition in the low load region where fuel consumption improvement is required while yet preventing knocking in the high load region, so implementation of such a technique has not been achieved. 
In view of the aforementioned problems, the present invention provides a control device for a spark ignition engine wherein the benefit of improved fuel consumption is produced by lean combustion and, in addition, the benefit of improved fuel consumption is increased by effectively performing compression ignition in a portion of the cylinders.