The unit impulse response of a system having transfer function K/(s+a) is shown below. The value of a is :

Time Response Analysis, Design Specifications and Performance Indices topics include: Standard test signals, time response of first and second order systems, steady state errors, performance indices, robotic control and state variable analysis. 1. Time response analysis is the study of a control system's response over time. The time response of a control system is the output of the system that varies with respect to time.  Time response specifications are important for the design and analysis of a system. Some time response specifications include: Rise time: The time it takes for the... Show more

Time Response Analysis, Design Specifications and Performance Indices topics include: Standard test signals, time response of first and second order systems, steady state errors, performance indices, robotic control and state variable analysis.

1. Time response analysis is the study of a control system's response over time. The time response of a control system is the output of the system that varies with respect to time. 

Time response specifications are important for the design and analysis of a system. Some time response specifications include:
Rise time: The time it takes for the response to rise from 10% to 90% of the final value
Delay time: The time it takes for the response to reach half of its final value from the zero instant
Peak time: The time it takes for the response to reach the first peak of the time response
Settling time: A specification that revolves around the speed of the system response
Peak overshoot: The deviation of the response at peak time from the final value of response 

The standard test signals used to know the performance of the control systems using time response of the output are: Impulse, Step, Ramp, Parabolic. 

2. Control system design specifications are quantitative measures that evaluate a control system's performance. These specifications can include: Error, Bandwidth, Rise time, Overshoot, Settling time. 

Control system specifications should be clear, realistic, and consistent with the system's requirements and constraints. 
Some design criteria for control systems include: Stability, Transient response, Steady state error, Some requirements for a control system include: Stability, Accuracy, Response, Speed of response 
Some basic elements and considerations for control systems include: Feedback, Objective control, Prompt reporting of deviations, Forward-looking control, Flexible controls, Hierarchical suitability, Economical control 

A Functional Design Specification (FDS) is a document that describes how a control system will operate. It can be passed between relevant team members, customers, and stakeholders for comment and review until the final document is agreed and signed off.

3. A performance index is a quantitative measure of a system's performance. It is used to specify a collection of performance objectives for the system. 

The performance index analysis of control systems is achieved by observing frequency-dependent plots of the singular values of certain characteristic matrices. These matrices are obtained as ratios of the plant and controller matrices. 
A system is considered an optimum control system when the system parameters are adjusted so that index reaches an extremum value, commonly a minimum value. 
When considering physical systems, there are also physical constraints like available power, maximum rotation speed, and other parameters. The actuation signal or error must be limited because you cannot just put in a lot of energy in your system. 

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