14th_Class_19-03-2024 Control systems.pptx

Here's the continuation of the report:

3.2.1 Parallel Plate Capacitor (continued)
As the IV fluid droplets move between the plates of the capacitor, the capacitance increases due to the change in the dielectric constant, resulting in the observation of a peak in capacitance.

3.2.2 Semi-cylindrical Capacitor
The semi-cylindrical capacitor consists of two semi-cylindrical conductors (plates) facing each other with a gap between them. The gap between the plates is filled with a dielectric material, typically the IV fluid.

When a potential difference is applied across the plates, electric field lines form between them. The dielectric material between the plates enhances the capacitance by reducing the electric field strength and increasing the charge storage capacity.

3.2.3 Cylindrical Cross Capacitor
The cylindrical cross capacitor is composed of two cylindrical conductors (rods) intersecting at right angles to form a cross shape. The space between the rods is filled with a dielectric material, such as the IV fluid.

When a potential difference is applied between the rods, electric field lines form between them. The dielectric material between the rods enhances the capacitance by reducing the electric field strength and increasing the charge storage capacity, similar to the semi-cylindrical design.

3.3 Advantages of Capacitive Sensing Approach
Capacitive sensing for IV fluid monitoring offers several advantages over other automated monitoring methods:

1. Non-invasive operation: The sensors do not require direct contact with the IV fluid, reducing the risk of contamination or disruption to the therapy.

2. High sensitivity: Capacitive sensors can detect minute changes in capacitance, enabling precise tracking of IV fluid droplets.

3. Low cost: The sensors can be constructed using relatively inexpensive materials, making them a cost-effective solution.

4. Low power consumption: Capacitive sensors typically have low power requirements, making them suitable for continuous monitoring applications.

5. Ease of implementation: The sensors can be easily integrated into existing IV setups without significant modifications.

6. Stable measurements: Capacitive sensors can provide stable and repeatable measurements across different IV fluid types.

Chapter 4: Experimental Setup and Results

4.1 Description of Experimental Setup
To evaluate the performance of capacitive sensors for IV fluid monitoring, an experimental setup was constructed. The setup included various capacitive sensor designs, such as parallel plate, semi-cylindrical, and cylindrical cross capacitors, positioned around an IV drip chamber.

The sensors were connected to a capacitance measurement circuit, which recorded the changes in capacitance as IV fluid droplets passed through the sensor's electric field. Multiple experiments were conducted using different IV fluid types and flow rates to assess the sensors' accuracy, repeatability, and sensitivity.

4.2 Measurements with

1. Updated New Syllabus UNIT III CLASS NO: 7 DATE:19-03-2024

2. First Order System & its Response Fig 1 : Block diagram of a 1 st order system Input Output Relationship:   Objective: To analyse the system responses to such inputs as the unit-step unit-ramp unit-impulse functions The initial conditions are assumed to be zero.

3. Unit Step Response of First Order System Input Output Relationship:     Laplace Transform of Input Signal Here it is       Using Partial Fraction Technique:     for   Time      

4. Interesting Observations: and The curve behaviour is exponential At The smaller the Time-Constant the faster the system response. The Slope of the Tangent Line at is since   ?

5. Unit-Ramp Response of First Order System Input Output Relationship:     Laplace Transform of Input Signal Here it is       Using Partial Fraction Technique:     for   Time    

6. Interesting Observations: The error signal       *** The error signal approaches to at steady state  

7. Unit-Impulse Response of First Order System Input Output Relationship:     Laplace Transform of Input Signal Here it is         for   Time      

8. An Important Property of Linear Time-Invariant (LTI) Systems for   for   for   Unit-Ramp Response Unit-Step Response Unit-Impulse Response Interesting Observations: d ( Unit-Ramp Response ) / dt = Unit-Step Response d ( Unit-Step Response ) / dt = Unit-Impulse Response The response to the integral of the original signal can be obtained by integrating the response of the system to the original signal and by determining the integration constant from the zero-output initial condition. This is a property of LTI systems. Linear time-varying (LTV) systems and nonlinear systems do not possess this property. Remark

9. Second Order System and Its Response Fig 2 : Servo system Simplified Block Diagram Plant

10. Relevant Equations related to Servo system ||Transfer Function of Servo system The equation for the load elements is   are inertia and viscous-friction elements denotes the Torque produced by the proportional controller whose gain is   Taking Laplace Transform of both side and considering initial conditions to be zero:       2 nd Order system Closed-Loop Transfer Function 2 Closed-Loop Poles  

11. Step Response of Second Order System   Closed-Loop TF   Closed-Loop Poles will be COMPLEX CONJUGATES if   Closed-Loop Poles will be REAL if   Remark: For Transient Response analysis, it is convenient to write     Key Terms : Attenuation : Undamped Natural Frequency : Damping Ratio : Actual Damping : Critical Ratio  

12.       Fig 3 : Standard Second-order feedback system Open Loop Transfer Function     3 Important Cases To Study Case 1: Underdamped ||   Case 2: Critically Damped ||   Case 3: Overdamped ||     Where,     Unit Step Function     Where,     Unit Step Function     Unit Step Function    

13. (A) STABILITY OF A MASS-SPRING-DAMPER System

14. (B) STABILITY OF A MASS-SPRING System

15. Expression of in all the cases   Case 1: Underdamped ||     Using Partial Fraction  

16. Important Observations of Case 2 Case 2: Critically Damped ||     Case 3: Overdamped ||    

17. Fig.: Unit-step response curves of the system A family of unit-step response curves with various values of w.r.t.  

18. Second Order System and Its Transient Response Specifications Salient Features: Frequently, the performance characteristics of a control system are specified in terms of the transient response to a unit-step input, since it is easy to generate and is sufficiently drastic. The transient response of a system to a unit-step input depends on the initial conditions. For convenience in comparing transient responses of various systems, it is a common practice to use the standard initial condition that the system is at rest initially with the output and all-time derivatives thereof zero. Then the response characteristics of many systems can be easily compared. The transient response of a practical control system often exhibits damped oscillations before reaching steady state. In specifying the transient-response characteristics of a control system to a unit-step input, it is common to specify the following: Delay Time Rise Time Peak Time Maximum Overshoot Settling Time  

19. Definitions: Delay Time   The delay time is the time required for the response to reach half the final value the very first time.   Example: For underdamped second-order system:

20. 2) Rise Time   The rise time is the time required for the response to rise from 10% to 90% , 5% to 95%, or 0% to 100% of its final value. For underdamped second-order systems, the 0% to 100% rise time is normally used. For overdamped systems, the 10% to 90% rise time is commonly used.   Example: For underdamped second-order system: Where; , And is shown here  

21. 3) Peak Time   The peak time is the time required for the response to reach the first peak of the overshoot. Example: For underdamped second-order system:

22. 4) Maximum % Overshoot   The maximum overshoot is the maximum peak value of the response curve measured from unity. If the final steady-state value of the response differs from unity, then it is common to use the maximum percent overshoot. Example: For underdamped second-order system: (A)

23. 4) Settling Time   The settling time is the time required for the response curve to reach and stay within a range about the final value of size specified by absolute percentage of the final value (usually 2% or 5%). The settling time is related to the largest time constant of the control system. Which percentage error criterion to use may be determined from the objectives of the system design in question. Example: For underdamped second-order system:

24. The relative dominance of closed-loop poles is determined by the ratio of the real parts of the closed-loop poles, as well as by the relative magnitudes of the residues evaluated at the closed-loop poles. The magnitudes of the residues depend on both the closed-loop poles and zeros. If the ratios of the real parts of the closed-loop poles exceed 5 and there are no zeros nearby, then the closed-loop poles nearest the axis will dominate in the transient-response behaviour because these poles correspond to transient-response terms that decay slowly . Those closed-loop poles that have dominant effects on the transient-response behaviour are called dominant closed-loop poles. Quite often the dominant closed-loop poles occur in the form of a complex-conjugate pair. The dominant closed-loop poles are most important among all closed-loop poles. Note that the gain of a higher-order system is often adjusted so that there will exist a pair of dominant complex-conjugate closed-loop poles. The presence of such poles in a stable system reduces the effects of such nonlinearities as dead zone, backlash, and coulomb-friction.   DOMINANT CLOSED LOOP POLES