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Note for Real Time Systems - RTS by rakesh chaudhary

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Rakesh Chaudhary
Rakesh Chaudhary
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Chapter-1 Introduction Real Time System: Any system in which the time at which output is produced is significant is called real time system. It is any information processing activity or system which has to respond to externally generated input stimuli within a finite and specified period. Generally, real-time systems are systems that maintains a continuous timely interaction with its environment as below. There are two types of real-time systems. 1. Reactive real time system 2. Embedded real time system  Reactive real-time system involves a system that has constant interaction with its environment for e.g. a pilot controlling an aircraft.  An embedded real-time system is used to control specialized hardware that is installed within a larger system for e.g. a microprocessor that controls the fuel-to-air mixture for automobiles. Real time is a level of computer responsiveness that a user senses as sufficiently immediate or that enables the computer to keep up with some external process for example, to present visualizations of the weather as it constantly changes. Real-time is an adjective pertaining to computers or processes that operate in real time. Real time describes a human rather than a machine sense of time. Examples of real-time systems include      Software for cruise missile Heads-up cockpit display Airline reservation system Industrial Process Control Banking ATM Real-time systems can also be found in many industries;     Defense systems Telecommunication systems Automotive control Signal processing systems Real Time System Compiled By: Loknath Regmi 1

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    Radar systems Automated manufacturing systems Air traffic control Satellite systems Digital Control: A digital control system model can be viewed from different perspectives including control algorithm, computer program, conversion between analog and digital domains, system performance etc. One of the most important aspects is the sampling process level. In continuous time control systems, all the system variables are continuous signals. Whether the system is linear or nonlinear, all variables are continuously present and therefore known (available) at all times. A typical continuous time control system is shown in Figure 1. Fig: A typical closed loop continuous time control system In a digital control system, the control algorithm is implemented in a digital computer. The error signal is discretized and fed to the computer by using an A/D (analog to digital) converter. The controller output is again a discrete signal which is applied to the plant after using a D/A (digital to analog) converter. General block diagram of a digital control system is shown in Figure 2. e(t) is sampled at intervals of T. In the context of control and communication, sampling is a process by which a continuous time signal is converted into a sequence of numbers at discrete time intervals. It is a fundamental property of digital control systems because of the discrete nature of operation of digital computer. Real Time System Compiled By: Loknath Regmi 2

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Sampled Data Systems: Long before digital computers became cost-effective and widely used, analog i.e., continuous time and continuous-state controllers were in use, and their principles were well established. A common approach be developed to design the digital controller that use the system that converts the analog version of system into a digital i.e., discrete-time and discrete-state version and resultant system is called sampled data system. The real-time (computing) system estimates from the sensor readings the current state of the plant and computes a control output based on the difference between the current state and the desired state (called reference input in the figure) called as control-law computation and corresponding controller is called digital controller. It typically samples (i.e., reads) and digitizes the analog sensor readings periodically and carries out its control-law computation every period. The sequence of digital outputs thus produced is then converted back to an analog form needed to activate the actuators. For example: Single-input single-output PID controller PID means Proportional, Integral and Derivative. In this controller, the analog sensor reading y (t) gives the measured state of the plant at time t. Let e (t) =r (t)-y (t) denote the difference between the desired state r (t) and the measured state y (t) at time t. The output u(t) of the controller depends on three terms as  a term that is proportional to e(t)  a term preoperational to the integral of e(t)  a term preoperational to the derivative of e(t) In the sampled data version, the inputs to the control-law computation are the sampled values yk and rk, k=0,1,2,.., which analog-to-digital converters produce by sampling and digitizing y(t) and r(t) periodically every T units of time then ek=rk-yk Real Time System Compiled By: Loknath Regmi 3

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is the k-th sample value of e(t). There are many ways to discretize the derivative and integral of e(t). For example, we can approximate derivative of e(t) for (k-1)T<=t<=kT by (ek-ek-1)/T By using the right rectangular rule of numerical integration to transform a continuous integral into a discrete as b  f ( x)dx  f (b)(b  a) a Suppose α, β, υ are some constants and they are chosen at the design time. During the k-th sampling period, the RTS computes the output of the controller according to this expression. kT k 0 i 1 uk  ek   (ek  ek 1 ) / T    e(t )dt  ek   (ek  ek 1 ) / T    eiT k 1 uk 1  ek 1   (ek 1  ek 2 ) / T    eiT i 1 Different discretization methods may lead to different expressions for uk, but they all are simple to compute and requires 10-20 machine instructions. The corresponding controller algorithms can be derived as: Set timer to interrupt periodically with period T At each timer interrupt, { do Do analog-to-digital conversion to get y Compute control output u Make digital-to-analog conversion and output u End do } Selection of Sampling Period: The length T of time between any two consecutive instants at which y(t) and r(t) are sampled is called the sampling period. T is a key design choice. The behavior of the resultant digital controller critically depends on this parameter. Ideally, we want the sampled data version behave like the Real Time System Compiled By: Loknath Regmi 4

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