Mapúa Institute of Technology School of Electrical, Electronics and Computer Engineering Feedback and Control Systems Laboratory ECE131L/B12
CONTROL SYSTEMS Module No.: 2 Systems Generation, Retrieval and Interconnection
Submitted by: Sapalaran, Ma. Carmela P.
Submitted to: Engr. Ernesto Vergara
Submitted on: August 6, 2015
Interpretation of Results Module 2 is about Systems Generation, Retrieval and Interconnection. The part 1 of the module is about generation of the transfer function on MATLAB with the use of tf(NUM,DEN) command, where NUM is the coefficient of the polynomial of the numerator while DEN is the coefficient of the polynomial of the denominator. This part also discusses the generation of the zero-pole-gain model by using the formula zpk(Z,P,K), where Z is the vector for zeroes, P is the vector for poles, and K is the vector for gain. The output of the zpk appears to be factored out polynomial for numerator and denominator. For generation of the state-space model, ss(A,B,C,D) command was used where A,B,C,D are matrices (vector quantities). For generation of frequencies with corresponding responses frd(Response, Frequencies) was used. The part 2 of the module is about Retrieval of the system. With the given generated transfer function, the coefficients of numerator and denominator was retrieve with the use of tfdata(H, ‘v’) command, where H is the given transfer function. For retrieval of the zero, pole, gain the zpkdata(H, ‘v’) command was used then the following set of zeroes, poles and gain was retrieve. For retrieval of state space parameters of the system, ssdata(H) command was used. Lastly the frequency response data of the system can be retrieve by the use of frdata(H) command, but since H is not an FRD data there’s no response and frequency retrieved. Based on the
observation, the commands for retrieval is similar to generation with the word “data” on it, so the memorization of the following command is easy. The part 3 of the module is about interconnection of systems. In this part the following block diagram must be reduced to a single transfer function. This part doesn’t depend on the command alone there is solving and critical thinking. If the two LTI model is in series connection the series(G1,G2) command is used where G1 and G2 are the transfer function. For parallel connection parallel(G1,G2) is used. Lastly for connection with feedback, feedback(G,H,SIGN) command was used, where G and H are the transfer function and feedback transfer function respectively, and SIGN depends on the polarity of the feedback that is either positive or negative feedback with the value of +1 or -1 respectively. This seatwork is about creating m-file with the given values of RLC circuit to generate and retrieve functions such as transfer function model, numerator, denominator, zero-pole-gain, and state-space model, etc. With a circuit given, the transfer function must be solve using KVL (note: this problem was solve on module 1). When the transfer function was solve the following command used in part 1 and part 2 of this module was used. When the m-file is executed, matlab must asked an input values for R, L, C and it will give the following values such as numerator, denominator, state-space model, etc.
Conclusion: Based on what I’ve learned from this module matlab can generate a transfer function using the sys=tf(num, dem) command where the num is the coefficient of the numerator while dem is the coefficient of the denominator in vector values. If the zero, pole, and gain is given, sys=zpk(Z,P,K) command is use to generate the function, where Z represent zeroes, P represent poles, and K represents gain. Where Z is in the numerator, P is in the denominator. If the system with matrices is given, state-space model can be generated using the command sys=ss(A,B,C,D), where A,B,C, and D represents the following matrices. If set of frequencies with corresponding system responses is given sys=frd(response,frequency) command is use to generate a tabulated form of the frequency response. I’ve also learned that matlab can retrieve the following parameters of the system. Using the [NUM,DEN]=tfdata(H, ‘v’) command the coefficient of the numerator and denominator can be extracted, where H is the given transfer function. To retrieve the gain, poles and zeroes of the system the [Z,P,K] = zpkdata(H, ‘v’) command is used.
To retrieve the state space parameters of the system the [A,B,C,D] = ssdata(H) command is used, the matrices are extracted from the given transfer function. To retrieve the frequency response data of the system [RESPONSE, FREQUENCY] = frdata(H) command is used but this command is only applicable for FRD data. I’ve also learned that matlab can solve a connecting systems. For LTI models with series connection, sys = series(G1,G2) command is used where G1 and G2 are the transfer function which are connected in series. For LTI models with parallel connection, sys=parallel(G1,G2) command is used where G1 and G2 are transfer function connected in parallel. Lastly for LTI models with feedback, sys= feedback(G,H,SIGN) command is used where G and H are transfer function in closed loop feedback configuration, and SIGN is the polarity of the feedback which has a value of +1 or -1.
