JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV DIGITAL CONTROL SYSTEMS Previous Question Paper (February/March - 2022 - R18)
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Main
Explain clearly the configuration of basic digital control scheme with the help of a neat block diagram. State its advantages and disadvantages.
Answer
A digital control system utilizes a digital computer or microcontroller as the controller to regulate the behavior of a continuous-time plant. The process involves converting analog signals from the plant into digital form, processing them according to a control algorithm, and converting the output back into analog form to drive the plant.
The basic configuration consists of the following components:
- Plant (Continuous-time system): The physical process being controlled, which operates in continuous time.
- Transducer/Sensor: Measures the output of the plant and converts it into an electrical signal.
- Analog-to-Digital Converter (ADC): Samples the continuous signal at discrete time intervals and quantizes it into a digital representation.
- Digital Controller: A computer or microprocessor that executes the control algorithm (e.g., PID, state-space control) based on the error signal.
- Digital-to-Analog Converter (DAC): Converts the digital control output back into a continuous analog signal.
- Zero-Order Hold (ZOH): Maintains the constant analog value between sampling intervals to provide a smooth input to the plant.
Block Diagram Description: The plant output is measured by a sensor, passed through an ADC to the digital controller. The controller compares the input reference with the feedback signal to generate a control signal, which is processed by a DAC and ZOH before being applied to the plant actuator.
Advantages:
- High flexibility as control laws can be modified by changing software code without altering hardware.
- Improved accuracy and reliability due to the elimination of component aging and drift associated with analog circuits.
- Capability to implement complex, non-linear, and adaptive control algorithms that are difficult or impossible to realize with analog components.
- Easy integration with data logging, monitoring, and communication networks.
Disadvantages:
- Requires high-speed ADC and DAC hardware, increasing system complexity and cost.
- Introduction of quantization errors and sampling delays, which can affect system stability and performance.
- Dependency on software reliability; bugs or processing delays can lead to catastrophic system failure.
- Requires careful selection of sampling frequency to satisfy the Nyquist-Shannon sampling theorem and avoid aliasing.
State different types of sampling operations. Discuss the effects of sampling.
Answer
Sampling operations are primarily categorized into three types based on the nature of the pulse train used for sampling:
- Ideal Sampling (Impulse Sampling): The continuous signal is multiplied by a train of unit impulses, resulting in a sequence of impulses whose areas are equal to the signal values at the sampling instants.
- Natural Sampling: The signal is multiplied by a train of pulses with finite width, where the top of each pulse follows the shape of the continuous signal during the pulse duration.
- Flat-Top Sampling: The signal is sampled by pulses of finite width, but the amplitude of each pulse remains constant at the value of the signal at the start of the sampling interval, creating a sample-and-hold effect.
The effects of sampling include:
- Aliasing: If the sampling frequency is insufficient, high-frequency components overlap with low-frequency components, causing distortion that cannot be reversed.
- Frequency Folding: The spectrum of the sampled signal becomes periodic, with replicas of the original signal spectrum centered at multiples of the sampling frequency.
- Information Loss: Sampling inherently discretizes time, and if the signal contains frequencies above the Nyquist rate, information is permanently lost.
Show that the sampling frequency should be at least twice the maximum frequency contained in the input signal.
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Obtain the Z-transform of
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Find the inverse z-transform of the following:
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State and explain Jury stability and analysis for the following characteristic equation.
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For the following discrete control system represented by:
Obtain the state representation of the system in the observable canonical form. Also find its state transition matrix.
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State and explain second method of Lyapunov used in stability analysis of discrete time control systems.
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Consider the system: X(k+1) = G X(k) + H U(k), where
Determine a suitable state feedback gain matrix K such that the system will have the closed loop poles at Z = 0.5 ± j 0.5 by using pole placement design technique.
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Explain the procedure of design of discrete output feedback controller for discrete time control systems.
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