I have a model for gear shift process including several fixed parameters, and other three variables x, y, and z, and I would like to develop a control to achieve successful engagement process.
The engagement process can be described by the shiftability condition f(x,y,z). So, given x,y,z, the system has two possibilities, successful (1) and unsuccessful (0) engagement.
However, x is a random variables in the interval [a, b], so, the engagement process is described now by the engagement probability P(y, z). So, given y, z, the engagement process now can be c successful (1) and (1 - c) unsuccessful (0), where c is the probability value.
Based on this, a controller reads (y) and output (z) should be developed to guarantee successful engagement (1). All what it can be done is based on y-value, the control can output z-value that can given the maximum possible engagement probability but the engagement process is still not 100% successful.
Does fuzzy logic, or Model protective control (MPC), or any other control method can achieve this task of 100% successful engagement, and How?
One cannot satisfy certain success without the control z being a function of both x and y. The issue only arises if one cannot dynamically measure x with the required accuracy. Here, the best we can do is maximize the probability of success, however, we can do a lot better than only considering y. If by randomness in x, you mean that we cannot measure x with a precision tighter than interval [a, b], the probability of success is integral a to b of f(x,y,z).PDF(x)dx. PDF(x) is the probability density function of x over the interval [a,b], which can be characterized by its mean, standard deviation, skewness, and so on in addition to a and b. I would use a controller based on y and the parameters that define the probability distribution of x (a and b at the least and desirably others) to maximize the probability of success.
Thank you Neetesh Sharma for your answer!
x is an angle and it is periodic in the interval [a, b]. x can be measured but the mechanical system that I am considering does not implement these sensors for some reasons.
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