Explain the concept of linear time-invariant (LTI) systems and their applications in control theory and signal processing.

The error signal that feeds the controller in a feedback control loop was recorded at various times, shown in Table 1. In open-loop mode, the magnitude of the signal feeding to the actuator was 12.0 mA at the instant when the controller was switched on at time zero.The steady-state process gain for the actuator, main process and sensor, considered as a single process, is 5.0 gpm/mA (a) Consider a P-only controller to be switched on and the proportional gain is0.3 mA/gpm.  What is the magnitude of the control signal sent to the actuator at 10 seconds? (b)  Consider a PI controller to be switched on; the proportional gain and inte-gral time are 0.3 mA/gpm and 6.0 seconds, respectively.  Estimate the magnitude of the control signal sent to the actuator at 25 seconds. (c) What do you think the controlled variable and its corresponding desired set point are?

Perform a 200-case Monte Carlo analysis of the DAC as shown and find the worst-case differential and integral linearity errors for the DAC. Use 10 percent resistor tolerances.

Drive an equation for linear signal conditioning that will convert a sensor output voltage in the spanning the range -1V to 3V into a -5V to 5V span. Also, design a circuit to do the corresponding transformation

Given a PI system with a proportional gain constant of 2 and an integral gain constant of 3. Initiallythe controller is running at a steady state output of 50%. For time = 0 to 1s there is no error. Fortime = 1s to 2s there is a constant error of +6%. For time = 2s to 3s there is an error of -4%. Findthe output of the controller at the end of each of the three time spans

9.1. Determine measures of performance in time-domain specification: a) percent overshoot, b) settling time with +/-5% tolerance, c) time to first peak, d) time to rise, e) delay time, f) oscillations period, and g) steady-state tracking error from data on figure below. 9.2. Identify the dynamics in terms of transfer function with estimated parameters. 3.928 0.5 2.72 2.5 2 1.5 3.5 3 output A input LS

after subpart f please!

Excercise 4: PI control for a first-order plant. Suppose you are to design a feedback controller for a first-order plant depicted in the figure below: Controller Plant К kp TS 1 S This configuration is referred to as a proportional-integral (PI) controller. You are to design the controller to satisfy some given time-domain specifications. (a) Find the (closed-loop) transfer function Gyr from r to y (see hw02). (b) Determine the steady-state error for a unit step input (Hint: e r - -y) (c) Find the transfer function Gun from n to u. (d) Determine k, and ki such that the feedback controlled system has damping ratio Ç = 0.5 and fre- quency wo. (Hint: the desired denominator polynomial for a closed-loop transfer function is of the form: d(s) s2+ 2Çwos +w2.) From now on, let K = 1, t = 1. (e) Find the values for kp and ki so that the frequency of the closed-loop system is 1, i.e. wo = 1. This controller will be referred to as controller 1. (f) Also, find the values for k, and k so that the…

Excercise 4: PI control for a first-order plant. Suppose you are to design a feedback controller for a first-order plant depicted in the figure below: Controller Plant К y и Кр TS1 ki This configuration is referred to as a proportional-integral (PI) controller. You are to design the controller to satisfy some given time-domain specifications. (a) Find the (closed-loop) transfer function Gyr from r to y (see hw02) (b) Determine the steady-state error for a unit step input (Hint: e r - y). (c) Find the transfer function Gum from n to u (d) Determine kp and ki such that the feedback controlled system has damping ratio Ç = 0.5 and fre- quency wo. (Hint: the desired denominator polynomial for a closed-loop transfer function is of the form: d(s) s22wos +w2.)