毕业（设计）论文英文翻译系 别专 业班 级学生姓名学 号指导教师报告日期International Railway JournalLevel Control System【Title】 International Railway Journal【Publication Date 】2008【No.】 period MarchIon Matei, Dumitru Popescu, Ciprian Lupu, llie LuicanPolitehnica University of Bucharest - Control and Computer Science FacultySplaiul Independentei nr.313,sector6,Bucurcsti,Romaniaemail: inion 3 home .ro1 Level control systemThe fluid flow is controlled by an electric pomp. The process input is a voltage with values between 0 and 10 V and the output is the fluid level measured by an ultrasounds transducer. The process is nonlinear but it is approximated with linear mathematical model around a representative point of functioning. The approximated mathematical model which was obtained using the sample period Te = 5s. It is important to mention that for designing a numerical regulator three steps must be followed:- computing the discrete model;- performances specification;- computing the adequate control algorithmIn this case for the level control were used the next numerical control algorithms: RST and PID with its two variants, PIDl and PID2. These algorithms have different performances so that the students will have the opportunity to compare them. First it will be presented the RST algorithm and than the paper will continue with PID algorithms which will be structured analyzed and compared to the first one.2 PID algorithmNumerical PID algorithm comes from sampling the continuous PID algorithm with all appropriate sampling period.Numerical PID controllers are suitable only for processes modeled by a second order transfer function with or without pure delay.It is worth to mention that some numerical PID controllers do not have a continuous equivalent.2.1 PIDl numerical algorithmLet us consider the algorithm:The transfer functions of a continuous PID controller，This algorithm is specified by four parameters:K - proportional action;Ti - integral action;Td - derivative action;Td - filtered derivative action.There are many methods that can be used to sample this algorithm resulting in a numerical controller of the same form.As it may be seen, PIDl numerical regulator has also four parameters (rth r1 r2, s1) as its continuous form. This algorithm can be International Railway Journalstructured in a RST form if T(q-1)=R(q-1 ).It is easy to notice that PIDl is one freedom degree algorithm. The transfer function in closed loop which join the reference r(t) with the output y(i) is, where P(q-1)defines the poles wanted in closed loop that determine the performances for perturbations rejection. PIDl algorithm introduces new zeros in closed loop by polynomial R(q-1) that alter the performances. This negative effect will be partially eliminated by thePID2 algorithm. Having already determined the RST algorithms it is now easy to calculate the PIDl parameters (if the rejection performances define by P (q-1) are not changed) because the polynomials R(q-1) and S(q-1) will be the same 3.As it may be observed in the next graphics the perforinanccs of the PIDl algorithm are inferior to the RST algorithm.2.2 PID2 numerical algorithmAs it was noticed above the PIDl regulator introduces supplementary zeros in closed loop by polynomial T(q-1)=R(q-1). Those zeros affect specially the control performances as it was observed in figure 7. This disadvantage can be partially eliminated if the polynomial T(q-1) is chosen. assuring in this manner a unitary transfer function in stationary regime 3.The block schematics of the PID2 numerical algorithm structured as RST is presented bellow.This algorithm assures superior performances compare to PIDl as it may be seen in the next graphics.3 RST numerical algorithmFor any control system there are defined two important objectives:1 . Reference s tracking;2 . Rejection of the perturbations;A classical control structure. with only one liberty degree (fig. 2) has the great disadvantage that it can not fulfill the two objective defined above.As it may be noticed the command is not pondered differentially by reference and measure. This means that some performances defined for perturbations rejection could restrict the reference tracking. If the polynomial R(q-1), which filter the reference, is replaced by another polynomial T(q-1) i t will lead to a RST structure with two liberty degree that accepts different performances in tracking and rejection3 4.The block structure of the RST numerical algorithm is presented in the next figure:The closed loop transfer function is:The performances for rejection are established by characteristic polynomial P(q-1) obtained by sampling a second order continuous system. The polynomials R(q-1) and S(q-1) results from solving the next polynomial equation:A(q-1)S(q-1)+ q-dB(q-1)R(q-1)= P(q-1) (4)The tracking performances are controlled by T(q-1) and refe