In this lab, you will design a PI controller to control the speed of a DC...
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In this lab, you will design a PI controller to control the speed of a DC motor. As you saw last week, the system of the driver and motor has an approximate transfer function of: For a reference voltage of 4V, C, is about 10 and C₂ is about 0.6s. The block diagram of the driver and motor with a PI controller is shown in Fig. 1. Step C₁ C₂s +1 Vin (Ref signal) Kp.s+Ki S dc motor+driver2 0.1 C1 C2.s+1 dc motor+driver Vout (Tacho) Fig. 1. Block diagram of the driver and motor with a PI controller. This week's prelab is in 3 parts and will take you through the process of designing a PI controller made of op amps, which you will implement in lab. Prelab: 1.) Find the transfer function of the system in Fig. 1. Write the transfer function in such a way that the denominator is a monic polynomial, i.e. the coefficient of the s² term is 1. It should look something like s² + as + b, where you find a and b in terms of KP, K₁, C₁, and C₂. Using what you have learned about second order systems, determine what the numerical values that a and b need to be for a rise time (tr) of 0.8s and an overshoot (Mp) of 20%. Using C₁ = 10 and C₂ = 0.6s, find Kp and K₁, and verify your choice with MATLAB. Are the rise time and overshoot exactly what you want? Explain why or why not. In this lab, you will design a PI controller to control the speed of a DC motor. As you saw last week, the system of the driver and motor has an approximate transfer function of: For a reference voltage of 4V, C, is about 10 and C₂ is about 0.6s. The block diagram of the driver and motor with a PI controller is shown in Fig. 1. Step C₁ C₂s +1 Vin (Ref signal) Kp.s+Ki S dc motor+driver2 0.1 C1 C2.s+1 dc motor+driver Vout (Tacho) Fig. 1. Block diagram of the driver and motor with a PI controller. This week's prelab is in 3 parts and will take you through the process of designing a PI controller made of op amps, which you will implement in lab. Prelab: 1.) Find the transfer function of the system in Fig. 1. Write the transfer function in such a way that the denominator is a monic polynomial, i.e. the coefficient of the s² term is 1. It should look something like s² + as + b, where you find a and b in terms of KP, K₁, C₁, and C₂. Using what you have learned about second order systems, determine what the numerical values that a and b need to be for a rise time (tr) of 0.8s and an overshoot (Mp) of 20%. Using C₁ = 10 and C₂ = 0.6s, find Kp and K₁, and verify your choice with MATLAB. Are the rise time and overshoot exactly what you want? Explain why or why not.
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here is detail solution TIS Vout Nout VIN denominat 7 Mp 20 2 from P 2 08 from C151 kp St ki C S kps... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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