Fitting non-linear equation to data using base R package

let say I have below data

Data = structure(list(col1 = c(31, 66, 88, 123, 249, 362, 488, 610, 
730, 842), col2 = c(2101.58953918969, 2103.57391509821, 2100.3292541732, 
2101.64107993765, 2100.51743895393, 2100.16708521627, 2102.1992412748, 
2101.06516854423, 2101.87929065226, 2101.25318636023)), row.names = c(NA, 
-10L), class = "data.frame")

Now I want to fit a non-linear equation as below -

library(stats)
nls(col2 ~ x1 + x2 / (1 + exp(-x3 * (col1 - x4))), data = Data, start = list(x1 = 0, x2 = 0, x3 = 0, x4 = 0), algorithm = "plinear")

However with this I am getting below error -

Error in qr.qty(QR.rhs, .swts * ddot(attr(rhs, "gradient"), lin)) : 
  NA/NaN/Inf in foreign function call (arg 5)

Can you please help me to understand what went wrong in my approach?

I want to use only base package to fit this equation as I can not download any contributed package from internet in my system.

Any pointer will be highly appreciated.

Solution

If I use SSfpl with your current data I can get an answer.

n1 <- nls(col2 ~ SSfpl(col1, A, B, m, s), data=Data)

pframe <- data.frame(col1=seq(0,900,length=101))
pframe$col2 <- predict(n1, newdata=pframe)

library(ggplot2); theme_set(theme_bw())
ggplot(Data, aes(col1,col2)) + geom_point() + geom_smooth() +
  geom_line(data=pframe, colour="red")

The parameterization is not quite the same as yours:

         A          B          m          s 
2001.56354 2002.06645  642.30178   20.76013

Based on x1 + x2 / (1 + exp(-x3 * (col1 - x4))),

I believe x4 = m (midpoint), x3 = s (scale), x1 = A (left asymptote), and x2 = B-A (B is the right asymptote).