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2.2 Transfer Functions To examine how the feedback loop and controller impacts a system we will...
4) A unity feedback control system shown in Figure 2 has the following controller and process with the transfer functions: m(60100c Prs(s +10(s+7.5) a) Obtain the open- and closed-loop transfer functions of the system. b) Obtain the stability conditions using the Routh-Hurwitz criterion. e) Setting by trial-and-error some values for Kp, Ki, and Ko, obtain the time response for minimum overshoot and minimum settling time by Matlab/Simulink. Y(s) R(s) E(s) Fig. 2: Unity feedback control system
4) A unity feedback...
D9.2 Design a state-feedback controller for the following systems. Determine the controller gains, open-loop transfer functions, and closed-loop transfer functions Use the open-loop transfer functions to obtain root locus, Bode plots, and gain and phase margins LU u=-kx + r Closed-loop poles at s --1tj 2
Q4. The feedback system shown below has a plant, a controller, and sensor transfer functions as G(s), Gc(s) and H(s), respectively. Find the output Y(s) and the input U(s) as a function of the inputs and transfer functions. (2 Points) D(s) R(s) + U(s) Gc (s) O G(s) - Y(s) H(S)
6) Consider the feedback system in Figure 1 with the loop transfer function a) [8 Marks] Plot the Bode diagram for this loop transfer function b) 10 Marks] Determine the frequency at which the gain has unit magnitude and compute the phase angle at that frequency. Controller Process G(s)Y(s) Figure 1
Consider the feedback sy PID COntroller Plant R(S) Y(s) the closed-loop transfer function T(s) = Y controller (Kp Find er p 1, Ks K ) and show that the system is marginally stable with two imaginary roots. (s)/R(s) with no sabl thosed-loop transfer function T(s) Y (S/R(s) with the (three- term) PID controller added to stabilize the system. suming that Kd 4 and K, -100, find the values (range) of Kp that will stabilize the system.
PD & PID controller design Consider a unity feedback system with open loop transfer function, G(s) = 20/s(s+2)(8+4). Design a PD controller so that the closed loop has a damping ratio of 0.8 and natural frequency of oscillation as 2 rad/sec. b) 100 Consider a unity feedback system with open loop transfer function, aus. Design a PID controller, so that the phase margin of (S-1) (s + 2) (s+10) the system is 45° at a frequency of 4 rad/scc and...
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2. a) A digital controller implementation for a feedback system is shown in Figure 2 where the sampling period is T0.1 second. The plant transfer function is s +10 P(s) = and the feedback controller, K, is a simple proportional gain (K>0).v R(z) E(z) S+10 Controller ZOH Plant Figure 2* i)o In order to directly design a digital controller in the z-domain, the plant P(s) 6. needs to be discretised as P(z). Find the ZOH...
a) Based on the following transfer functions, use a model-based controller design method to design a feedback controller with te- i.e. determine the controller parameter value(s) 4 G, 3 G0.5 (4 marks) b) Determine the response y(t) to a unit step change disturbance of the closed loop transfer function from part a) implementing the controller from part a). Show al your working (you may refer to entries in the table of Laplace transforms attached as part of your working) (5...
5. Consider the feedback control system shown below with constant reference w, and constant disturbance d. Show that the steady-state error e(0o) lm()is zero when k>0 and is given by (wr +Kd)/(Kkp +1) when k0 Lu TS+ Figure 1: Speed regulation of DC motor using PI controller
2) Sketch the phase portrait of the system x' (t) = Ax (t) if (a) 5= [ 9), P=[7"}] (1) 5= [ • ? ], P=[} >>]