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- 2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2The temperature of a catalysed exothermic reaction is being maintained at T1°C as it promotes generation of a particular product. It is proposed to control the temperature with a proportional only controller of gain Kc. The temperature dynamics of the reactor can be modelled as a mixture of a CSTR (1st order) and PFR (dead time) to changes either in inlet temperature, or in the heating/cooling jacket flowrate via Ke-tas Ts+1 i) Considering a change in inlet temperature show why a 1st order model for a CSTR and a dead time model for a PFR are appropriate. CSTR - continuous stirred tank reactor PFR - plug flow reactor8 15 10 The figure below represents a time response of a control system. What is it? * Unit-step response of a Prototype First-Order System; Unit-Impulse Response of a Prototype First-Order System: Unit-Step Response of a Prototype Second-Order System: Unit-Impulse Response of a Prototype Second-Order System. apnaduy
- PleaseA thermocouple is connected to a data acquisition system which is used to measure temperature of air in a duct. For a step-input, the system measures the temperature accurately at steady state. Assume the dynamics of the sensor(thermocouple) limit the system's speed of response. The sensor has a time constant of 0.5 sec. In a given situation, the duct's air temperature varies with time as a sinusoid of frequency 2 rad/s with amplitude of 10°C. In this case, the measured temperature by the system is a sinusoid as wellI, as a function of time. The amplitude of this (measured) sinusoid, at steady-state, is closest to: Select one: а. 10°C b. 5°C С. 3°C O d. 7°CAn experiment was carried out on a SDOF system to estimate the natural frequency and damping. The time history plotted below has the response in centimetres and the time in seconds, as shown in Figure Q10 below. Estimate values for the following and choose the nearest values from the list given below: the damped natural frequency in Hz; the damping ratio using the logarithmic decrement method; and the natural frequency in rad/s. Ju(t) 2.00 AMA 1.00 0.00 0.00 Figure Q10 0.80 1.60 Select one or more: O a. 4.92 b. 0.781 c. 0.625 O d. 0.330 O e. 0.052 2.40 3.20 4.00 t
- Amplitude Given the system unit-step response, determine maximum overshoot, settling time and steady-state error * 1.4 1.2 0.8 0.6 0.4 0.2 0,35 0.05 0.1 Step Response 0.15 0.2 Time (sec) 0.25 0.3 0.35The temperature of a catalysed exothermic reaction is being maintained at T1°C as it promotes generation of a particular product. It is proposed to control the temperature with a proportional only controller of gain Kc. The temperature dynamics of the reactor can be modelled as a mixture of a CSTR (1* order) and PFR (dead time) to changes either in inlet temperature, or in the heating/cooling jacket flowrate via Ke-'a® Ts+1 i) Considering a change in inlet temperature show why a 1st order model for a CSTR and a dead time model for a PFR are appropriate. CSTR - continuous stirred tank reactor PFR - plug flow reactorMA Figure (2) 3- The time response of a liner spring-mass-damper system with the mass of (m), the stiffness coefficient of (k), and a dampirg constant of (c) is given below in figure (2) with a set of coordinates marked by fillec circles. x(t) is in meters, it is in seconds. Indicate the units of all quantities involved in your solutions when calculate 0 -1- (0.53, 1.78) (0,0.8) 2 (2.1,-1.3) (3.7,0.9) L 4 (5.3,-0.7) - The damping ratio of the system. Its natural frequency w., damping corstart c, and stiffness coefficient k; for (m-1.25 kg). III- The amplitude of the motion if the phase angle is given as (0.4 rad). IV. Its initial conditions. (6.86, 0.5) 10 t[sec]
- The response of a system 1s given by x(t) = 0.003 Cos Böt +0.0045in 30t m. Defermine the amplitude Og motion, the frequency in Hz, the frequency in rad/s, the frequency n rpm, the phase angle and the responce in the form of x(t)= Asn(wk tp) og mction, the period1 Problem 5 4 State, x(t) SAWNO-Nw. ● ● Case 1 O 2 6 Time, sec. underdamped critically damped State, x(t) • overdamped 54321 ONS TY Case 2 2 ▷ Time, sec. 8 10 State, x(t) 5 2 + 3 4 Case 3 2 ▷ 6 Time, sec. 5432 State, x(t) & A & No. 2 Match each of the resposes above to one of the following second-order system types: • undamped Case 4 ▷ Time, sec.1 Problem You are given the following data (below) showing the steady-state output response, x(t), of a mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot is the response after all the transients have decayed (the time is shifted to start at zero for conve- nience). x 0.5225 Displacement pu(t) Sinusoidal force input x 0.1041 1.5 1 Y2 х 0.2783 Y1.372 0.5 h ok -0.5- -1 -1.5 x(t) M Assume: bl u(t) x(t) Horizontal Plane (no gravity) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec) www k Using only the data provided above (the blue line is the input u(t) and the red line is the output x(t)), determine: 1. The frequency of the input in rad/s 2. The amplitude of the input, A 3. The frequency of the output in rad/s 4. The output-input ratio |G(iw)| = max(x(t)) max(u(t))' at the particular input frequency shown. 5. The phase (also called phase lag) of the output, $, at the particular input frequency shown in degrees. Note the phase is generally…