Exact Deadbeat Controller Design From N Impulse Response Samples

1986 ◽  
Vol 108 (1) ◽  
pp. 65-68 ◽  
Author(s):  
R. E. Rink
Keyword(s):  
Steady State ◽  
Impulse Response ◽  
Controller Design ◽  
Open Loop ◽  
Step Response ◽  
Simple Method ◽  
Arbitrary Type ◽  
Pi Controllers ◽  
State Tracking ◽  
Time Invariant

A simple method is given for the design of exact deadbeat regulators and PI controllers when only N impulse or step response samples from the process are available. It is required that the process be linear, controllable, observable, time invariant, and that N≥2n, where n is the degree of the process. It is not required that the process be open-loop stable, in distinction with previously-given simple methods. This makes it easy to include any number of integrations in the controller to achieve steady-state tracking properties of arbitrary type.

scholarly journals Global Systems for Mobile Position Tracking Using Kalman and Lainiotis Filters

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Impulse Response ◽  
Finite Impulse Response ◽  
Position Tracking ◽  
Computational Burden ◽  
Time Invariant ◽  
Global Systems

We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which describe the movement inx-axis andy-axis simultaneously or separately. We present the time invariant filters as well as the steady state filters: the classical Kalman filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both proposed models but have different computational burden. Finally, we propose a Finite Impulse Response (FIR) implementation of the Steady State Kalman, and Lainiotis filters, which does not require previous estimations but requires a well-defined set of previous measurements.

scholarly journals Optimizing the Parameters of Sliding Mode Controllers for Stepper Motor through Simulink Response Optimizer Application

2021 ◽  
Vol 1 (2) ◽  
pp. 209-225
Author(s):  
Magdi Sadek Mahmoud ◽  
Ali H. AlRamadhan
Keyword(s):  
Steady State ◽  
Sliding Mode ◽  
Open Loop ◽  
Step Response ◽  
Stepper Motor ◽  
Model Parameters ◽  
Response Requirement ◽  
Load Torque ◽  
Sliding Mode Controllers ◽  
Motor Model

This paper will focus on optimizing parameters of sliding mode controllers (SMC) for hybrid stepper motor models simulated in Matlab/Simulink. The main objective is to achieve a smooth transient and robust, steady-state to track reference rotor position when the stepper motor is subjected to load disturbances. Two different structures of SMC controllers will be studied, which are based on the flat system concept that is applicable to the stepper motor model. The hassle to determine controller parameters will be optimized using the Simulink Response Optimizer application.  The performance of the controllers will be evaluated by considering load torque and variation in the model parameters. Although the results showed that an open-loop controller could move the rotor to the desired position, however, the transient response had undesired oscillations before the output settled at the steady state. The response was improved by optimizing SMC controllers’ parameters to meet the desire step response requirement. Despite both SMC methods have successfully tracked the reference, there are some challenges to deal with each method in regard to the state measurements, the number of optimized controllers’ parameters, and the scattering of control inputs.

scholarly journals System Dynamics and Control of a Linear Compressor for Stroke and Frequency Adjustment

2001 ◽  
Vol 124 (1) ◽  
pp. 176-182 ◽  
Author(s):  
B. J. Huang ◽  
Y. C. Chen
Keyword(s):  
Control System ◽  
Steady State ◽  
System Dynamics ◽  
Controller Design ◽  
Tracking Error ◽  
Step Response ◽  
System Dynamics Model ◽  
Dynamics Model ◽  
Linear Compressor ◽  
Frequency Adjustment

This paper presents results of an investigation on the system dynamics and the controller design of a linear compressor for stroke and frequency adjustment. A system dynamics model was derived and identified experimentally. A control system was designed based on the system dynamics model. The control system used a PDF (Pseudo-Derivative-Feedback) algorithm. The results of step response test for stroke regulation show that, it takes about 0.2 s for the regulation with small overshoot and negligible steady-state error. For the step change of operating frequency, it takes about 0.4 s to reach steady state with small tracking error. The control system also has very good performance for disturbance rejection. The transient periods are about 0.2 s with stroke variation to within 10%. The controller is shown to have the capability to replace the conventional crank-shaft mechanism as in a reciprocating compressor. The controller can also be used to regulate both stroke and frequency of the compressor during operation. The performance can thus be very flexible and efficient for a system using the linear compressor and the present control system.

Evaluation of fractional order of the discrete integrator. Part II

2020 ◽  
Vol 23 (2) ◽  
pp. 408-426
Author(s):  
Piotr Ostalczyk ◽  
Marcin Bąkała ◽  
Jacek Nowakowski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Output Signal ◽  
Linear Time ◽  
Mathematical Problem ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Input And Output ◽  
Order Difference Equation ◽  
Time Invariant ◽  
Discrete Integrator

AbstractThis is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Impedance Reduction Controller Design for Mechanical Systems

2013 ◽  
Author(s):  
Hanseung Woo ◽  
Kyoungchul Kong
Keyword(s):  
Case Studies ◽  
Closed Loop ◽  
Controller Design ◽  
Mechanical Impedance ◽  
Open Loop ◽  
Mechatronic Systems ◽  
Closed Loop Systems ◽  
Guaranteed Stability ◽  
Reaction Forces ◽  
Definition Of

Safety is one of important factors in control of mechatronic systems interacting with humans. In order to evaluate the safety of such systems, mechanical impedance is often utilized as it indicates the magnitude of reaction forces when the systems are subjected to motions. Namely, the mechatronic systems should have low mechanical impedance for improved safety. In this paper, a methodology to design controllers for reduction of mechanical impedance is proposed. For the proposed controller design, the mathematical definition of the mechanical impedance for open-loop and closed-loop systems is introduced. Then the controllers are designed for stable and unstable systems such that they effectively lower the magnitude of mechanical impedance with guaranteed stability. The proposed method is verified through case studies including simulations.

Model-Matching Controller Design With Input-Output Data—A Numerical Approach for Redundantly Actuated Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 800-805
Author(s):  
Jenq-Tzong H. Chan
Keyword(s):  
Explicit Knowledge ◽  
Controller Design ◽  
Numerical Technique ◽  
Open Loop ◽  
Loop System ◽  
Synthesis Process ◽  
Model Matching ◽  
Input Output ◽  
Output Data ◽  
Redundantly Actuated

A numerical technique for control system synthesis based on input-output data is presented. The method is applicable when the system is open-loop stable and redundantly actuated. The major merits of the method are as follows. First, the closed-loop system equation may be arbitrarily assigned. Second, explicit knowledge of an open-loop system model is not needed for controller synthesis. Third, the stability of the synthesized system may be verified during the synthesis process; hence, the workability of the controller is ensured.

Study of Temperature Effect on Servovalve-Controlled Fuel Metering Unit

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Bin Wang ◽  
Haocen Zhao ◽  
Ling Yu ◽  
Zhifeng Ye
Keyword(s):  
Steady State ◽  
Temperature Variation ◽  
Dynamic Characteristics ◽  
Numerical Study ◽  
Step Response ◽  
Fuel Temperature ◽  
Wide Range ◽  
Fuel Rate ◽  
Testing Condition ◽  
The Given

It is usual that fuel system of an aero-engine operates within a wide range of temperatures. As a result, this can have effect on both the characteristics and precision of fuel metering unit (FMU), even on the performance and safety of the whole engine. This paper provides theoretical analysis of the effect that fluctuation of fuel temperature has on the controllability of FMU and clarifies the drawbacks of the pure mathematical models considering fuel temperature variation for FMU. Taking the electrohydraulic servovalve-controlled FMU as the numerical study, simulation in AMESim is carried out by thermal hydraulic model under the temperatures ranged from −10 to 60 °C to confirm the effectiveness and precision of the model on the basis of steady-state and dynamic characteristics of FMU. Meanwhile, the FMU testing workbench with temperature adjustment device employing the fuel cooler and heater is established to conduct an experiment of the fuel temperature characteristics. Results show that the experiment matches well with the simulation with a relative error no more than 5% and that 0–50 °C fuel temperature variation produces up to 5.2% decrease in fuel rate. In addition, step response increases with the fuel temperature. Fuel temperature has no virtual impact on the steady-state and dynamic characteristics of FMU under the testing condition in this paper, implying that FMU can operate normally in the given temperature range.

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