• Convert PDF to Linearized PDF in C#


    Linearized PDF files are a special format of PDF files that can be viewed more quickly over the Internet. Linearized PDFs, in the case of a large number of pages, can highlight the advantages of fast browsing. The following is a method to convert a PDF file to a linearized PDF through a back-end .NET […]

  • [data system distributed system] consistency and consensus


    Now, we discuss the relevant algorithms and protocols for building fault-tolerant distributed systems. In order to build a fault-tolerant system, it is best to establish a set of general abstract mechanisms and corresponding technical guarantees, so that various applications on it can safely rely on the underlying guarantees. This is the same as the principle […]

  • Mathematical basis of vehicle control theory — state equation


    1. Use the equation of state to find the transfer function formula The equation of state is\(G(s)=\dfrac{Y(s)}{U(s)} = C(sI-A)^{-1}B+D\) Example 1:\(m-c-k\)System, seeking\(m\overset{··}{x}+c\overset{·}{x}+kx=f\)Transfer function.Solution:order\(x_1 = x\),\(x_2=\overset{·}{x}\)Then there are: \[\begin{cases} \overset{·}{x_1}=x_2\\ \overset{·}{x_2}=\dfrac{1}{m}[-c x_2-k x_1]+\dfrac{f}{m} \end{cases}\] According to the vector expression of the state equation and the vector expression of the output equation \[\begin{cases} \overset{·}{X} = AX+Bf \\ […]