Distributed Real-Time Control Systems
Distributed Real-Time ControlSystemsModule 7Digital PI Control1
PI ControluffKprufbe-PI Control:Ki/sduSysyuintuf b (t) Kp e(t) KiZte( )d t02
Digital PI Controller Discretizatione(t) r(t)Continuous model:y(t)uf b (t) Kp e(t) KiConsider the integral term and its derivative:uint (t) KiZtt0Then:Ki e(t) te( )d t0duint (t) Ki e(t)dte( )d Approximate the derivative- valid for small T- k is the discrete time variableZduint (t)uint (t) dtuint (t)uint (tTuint (tTT)T)3
Uniform Samplingt kTTT2T .(k-1)T kTKi e(kT ) .tk – Discrete time variableT – Sampling TimeKi e(t) (k 1)Tuint (t)uint (kT )uint (tTuint ((kTT)1)T )4
Digital PI AlgorithmKi e(kT ) uint (kT )uint (kT ) uint ((kuint ((kT1)T )1)T ) Ki T e(kT )Joining the proportional term, we get:uf b (kT ) Kp e(kT ) uint (kT )5
Computer ImplementationDigital representation:f (kT ) f iuint[k-1]z-1uint [k] uint [k1] T Ki e[k]uf b [k] Kp e[k] uint [k]6
Pseudo Codeuint [k] uint [k1] T Ki e[k]uf b [k] Kp e[k] uint [k]At each sampling time do:– Read variable y from A/D port– Compute error e r – y– Compute control:ui ui before T*Ki*e;ui before ui;u Kp*e ui;– Write u at the D/A port.– Wait until next sampling time.7
Minimal Implementation in Arduino IDEconst int LED PIN 15;float ui before {0.0};const float p gain {0.0};const float i gain {30.0};const float samp time {0.01}; //10msconst float reference {1500};void setup() {analogReadResolution(12); //12 bit resolution (default is 10 .)analogWriteFreq(30000); //30KHzanalogWriteRange(4095); //Max PWM value (correspods to 100%)}void loop() {float y analogRead(A0);float time now micros();float error reference - y;float ui ui before samp time*i gain*error;float u p gain*error ui;if( u 0) u 0;if( u 4095 ) u 4095;int pwm (int)u;analogWrite(LED PIN, pwm);ui before ui;delay(10);}8
Tuning the PI controller Manual method is OK. Start with small values for Kp and Ki such thatthe system is slow to react to disturbances butdoes not overshoot or oscillate. Increase the gains to make it faster, if needed,but still avoid overshoot and oscillations. Find the best combination of Kp and Ki forsmooth and reasonably fast performance.9
Dangers of Integral ControlEvery actuator has limits!Problematic for controllers with integral action.-Controller withIntegral ActionuWhen the control signal saturates, the integral part keeps integrating. Known asintegrator-windup or reset-windup**.**an integrator is often denoted by “reset” due to its effect in the controller. Whenappropriatelly used, it “resets” the tracking errors.10
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Windup Effect on a Motor Drive12
Anti-WindupSome Windup solutions: Setpoint and Setpoint rate limitation Slows down system response. Does not prevent windup due to disturbances. Reset integral term Generates discontinuities in the command. Saturate the integral term Must compute the right saturation limits. Back-Calculation (slow discharge integrator) Must tune one parameter.13
Integral ResetWhen the output saturates, the integral term in the controller is set to zeroKi/suiuffufbother feedback termswumaxusatuuminif ( (u umax) (u umin) )ui 014
Saturate Integral TermWhen the output saturates, the integral term in the controller is recomputed sothat its new value gives an output at the saturation limit.Ki/suiuffufbother feedback termsumaxusatuwuminif (u umax)ui umax – uff – wif (u umin)ui umin – uff – w15
Back CalculationSame objective as before, but the discharge of the integral term is dynamical.eseuff1/TtKi/sumaxufbuiuuminwCompute the saturation limits of ui: uimax umax – uff - wuimin umin – uff - wCompute the saturation of ui:uisat sat(ui , uimin, uimax)Compute the saturation error: es ui - uisatDischarge the integrator at rate es/Tt16
PID Anti-Windup SimulationSCDTR 2013/2014 - Lecture 5A. Bernardino, C. Silvestre, IST-ACSDC17
Without Anti-Windup18
With Anti-Windup19
Introduction of the Reference dff (xdes ) ydesDesiredObservation-Noiseuẋ f (x, u) dSystem to controlnxh(x, u) ySensorfb (xdes , f the reference of the feedback controller is the desired final value, thesystem may over-react to changes in setpoint, because bothfeedforward and feedback controllers are forcing a new set-point.20
Blending Feedforward and Feedback Turn off feedback while the response to feedforwardstabilizes – only possible with open loop stable systems. Define smoother (non-discontinuous) feedforwardcommand. Generates smaller feedback errors anddiminishes overreactions. Define a smother reference for the feedback term – ideallythe same signal as the expected system output.21
Decoupled Feedforward ncedff (xdes ) � f (x, u) dSystem to controlnxh(x, u) ySensorfb (xdes , nstead, the reference to the feedback controller should be the predictedobservation (trajectory) in case of no disturbances.If the system simulator is perfect, the error term should be close to zero.22
Decoupled Feedforward Feedback The best of both worlds– Feedback attenuates disturbances and noise.– Feedforward drives the system to the set point.23
Distributed Real-Time Control Systems Module 7 Digital PI Control 1. PI Control 2 PI Control: Sys K p K i/s-r u ff u fb d y u int e u u . stabilizes -only possible with open loop stable systems. Define smoother (non-discontinuous) feedforward command. Generates smaller feedback errors and
Distributed Database Design Distributed Directory/Catalogue Mgmt Distributed Query Processing and Optimization Distributed Transaction Mgmt -Distributed Concurreny Control -Distributed Deadlock Mgmt -Distributed Recovery Mgmt influences query processing directory management distributed DB design reliability (log) concurrency control (lock)
1.1 Hard Real Time vs. Soft Real Time Hard real time systems and soft real time systems are both used in industry for different tasks [15]. The primary difference between hard real time systems and soft real time systems is that their consequences of missing a deadline dif-fer from each other. For instance, performance (e.g. stability) of a hard real time system such as an avionic control .
Introduction to Real-Time Systems Real-Time Systems, Lecture 1 Martina Maggio and Karl-Erik Arze n 21 January 2020 Lund University, Department of Automatic Control Content [Real-Time Control System: Chapter 1, 2] 1. Real-Time Systems: De nitions 2. Real-Time Systems: Characteristics 3. Real-Time Systems: Paradigms
In the design of distributed systems it is important that the real-time conditions must be strictly adhered. In order to model the real-time conditions of distributed systems an integrated model of distributed application and communication has been presented in [12]. In the model the distributed control application is split into several parts
Distributed Control 20 Distributed control systems (DCSs) - Control units are distributed throughout the system; - Large, complex industrial processes, geographically distributed applications; - Utilize distributed resources for computation with information sharing; - Adapt to contingency scenarios and
Abstract. Concurrency control is one of the main issues in the studies of real-time database systems. In this paper di erent distributed con-currency control methods are studied and evaluated in real-time system environment. Because optimistic concurrency control is promising candi-date for real-time database systems, distributed optimistic .
distributed control approach. The concept of a distributed controller is widely accepted in motion control and factory automation systems [9]. More along the lines of distributed control at the converter level was reported by Malapelle et al. [7] who proposed a distributed &@tal controller for hgh-power drives. They
Screw-Pile in sand under compression loading (ignoring shaft resistance) calculated using Equation 1.5 is shown in Figure 3. The influence of submergence on the calculated ultimate capacity is also shown. The friction angle used in these calculations is the effective stress axisymmetric (triaxial compression) friction angle which is most appropriate for Screw-Piles and Helical Anchors. 8 .
