Adding SOS state vector initialization in gas inj

While computing gas injection, when low pass filter is applied to the
flow rate, it would show a transient if the flow rate starts at a
non-zero value. This could be bad for MPC which uses the computation
while optimization. To avoid this, we initialize the state vector of
the low pass filter to the initial value of the flow rate. This way,
there will never be an initial transient due to the low pass filter.

src/gas_injection.jl

@@ -230,7 +230,7 @@ function compute_gas_injection(
             )
         end
         if !isnothing(LPF)
-            flow_rate = filt(LPF, flow_rate)
+            flow_rate = filt(LPF, flow_rate, create_si(LPF, flow_rate[1]))
         end
         flow_rate = map((x)::Float64 -> x < 0.0 ? 0.0 : x, flow_rate)
         future_flow_rates = flow_rate[end-skip+2:end]
@@ -345,6 +345,36 @@ function get_lpf(
     return convert(SecondOrderSections, bilinear(filter_s, fs))
 end
 
+"""
+    create_si(filter, last_val)
+
+Create initial state for a filter based on a provided last value. This assumes that
+upto this point, there was a constant command on (called prev_xi in this code) and the
+filter had reached equilibrium to a constant output which is the last_val provided.
+"""
+function create_si(filter::SecondOrderSections, last_val::Float64)
+    n = length(filter.biquads)
+    g = filter.g
+    si = zeros(Float64, 2, n)
+    for fi ∈ n:-1:1
+        b0 = filter.biquads[fi].b0
+        b1 = filter.biquads[fi].b1
+        b2 = filter.biquads[fi].b2
+        a1 = filter.biquads[fi].a1
+        a2 = filter.biquads[fi].a2
+        if fi == n
+            prev_yi = last_val / g
+        else
+            prev_yi = last_val
+        end
+        prev_xi = prev_yi * (1 + a1 + a2) / (b0 + b1 + b2)
+        si[2, fi] = b2 * prev_xi - a2 * prev_yi
+        si[1, fi] = si[2, fi] + b1 * prev_xi - a1 * prev_yi
+        last_val = prev_xi
+    end
+    return si
+end
+
 """
     dribble(
         data::Vector{Float64},