pid control output problem

to tune the pid controller i have make a matlab model for the quadrotor that have 4 inputs (angular velocity of motor) w1 w2 w3 w4

i have 4 pid : altitude controller with the output u1 roll controller with the output u2 pitch controller with the output u3 yaw controller with the output u4

we have that

b=trust factor d=drag factor

w1^2=(1/4*b)*u1 + (1/2*b)*u3 + (1/4*d)*u4 w2^2=(1/4*b)*u1 - (1/2*b)*u3 + (1/4*d)*u4 w3^2=(1/4*b)*u1 + (1/2*b)*u2 - (1/4*d)*u4 w4^2=(1/4*b)*u1 - (1/2*b)*u2 - (1/4*d)*u4

so to get w1 w2 w3 w4 we use sqrt() but the problem the pid output can be negative so when we use sqrt it will give complexe number. please help me to solve this problem thank you

[Omanshu Thapliyal]

It would help if you could provide some more information about the variables in the equation (the units, what they stand for, and the reference for the equation). Also, assuming the equation is correct, a source for getting negative values to (w_i)^2 for i = 1,2,3,4 could be that you are using unbounded control inputs 'u', while actually they would be bounded.