The transfer function of the system numerically become
The state space model become
  1. Proposed Controllers Design
  2. H infinity Mixed-Sensitivity Controller Design
H infinity mixed-sensitivity evaluates a controller K that minimizes the H infinity norm of the closed-loop transfer function the mixed weighted sensitivity
Where S and T are referred to as the sensitivity and complementary sensitivity, respectively. R measures the manipulate effort. The again controller K is such that S, R, and T fulfill the following loop-shaping inequalities:
Where = GAM. Thus, the inverses of W1 and W3 determine the shapes of sensitivity S and complementary sensitivity T. Typically, you choose a W1 this is large within the desired manipulate bandwidth to acquire accurate disturbance attenuation (i.e., performance). Similarly, you commonly pick a W3 that is large outside the manage bandwidth, which facilitates to make sure precise stability margin. The solenoid based linearly movable armature system with H infinity mixed sensitivity controller block diagram is shown in Figure 2 below.