Practical Control System Design: Classical & Modern Methods

At the beginning of a control engineering investigation is the modelling of the given system. Based on the physical laws, a system description, usually mathematical, is derived that describes the cause-effect relationships between the inputs u and the outputs y. The system is then modelled. Matlab provides the following representation types for continuous-time and discrete-time linear time-invariant systems (LTI systems):Transfer Function TF,Zero-Pole-Gain ZPK.

The state space is another way of describing a dynamic model of the system, and it can be used to represent not only linear systems but also nonlinear systems. The state space representation of a system is always referred to as the internal model description because the internal variables, such as the states, are fully described in such a model representation. Matlab provides the following representation type for continuous-time and discrete-time linear time-invariant systems (LTI systems):State representation (State-Space SS)

Discrete-time representation of LTI models,Discrete-time transfer function in DSP format,Time delays in LTI models,Conversion to another LTI model type,Modeling of Interconnected Block Diagrams

It is often necessary to convert a continuous-time system into a discrete-time system or vice versa. For example, when results from a simulation are to be compared with (sampled) measurement data or when problems associated with the sampling itself are of interest.

MATLAB Control System Toolbox part I memorization

all important topics are checked again in order to memorise the functions of the control system toolbox:

modeling, transfer functions, state space model,Creation of LTI-Models,Discrete-time LTI-Models,Working witch LTI-Models.

Once a control system has been modelled, the second step is to examine the system properties. In order to make statements about the behaviour of a system, the Control System Toolbox provides a comprehensive spectrum of analysis functions: from the general system properties to model dynamics in the time and frequency range to checking the controllability.

now we will present time domain analysis of linear systems. This enables us to obtain and sketch the step response, impulse response, and time transient response to any input signal. This is proved to be an effective and straightforward way to describe the behavior of the systems.

The system behaviour in the frequency range is also interesting for the control engineer: Often the test signals are sinusoidal or the parameters of the system are not exactly known. By means of the methods for frequency response investigation, very extensive statements can be made about frequency-dependent system properties

By means of the methods for frequency response investigation, very extensive statements can be made about frequency-dependent system properties: stationary DC gain, bandwidth, amplitude and phase margin, stability of the closed control loop.

The Linear System Analyzer app lets you analyze time and frequency responses of LTI systems.

Root locus, a graphical presentation of the closed-loop poles as a system parameter is varied, is a powerful method of analysis and design for stability and transient response (Evans, 1948)

Control System Toolbox provides algorithms and apps for systematically analyzing, designing, and tuning linear control systems. You can tune compensator parameters using interactive techniques such as Bode loop shaping and the root locus method. The toolbox automatically tunes both SISO and MIMO compensators, including PID controllers. The Control System Designer app lets you design single-input, single-output (SISO) controllers for feedback systems modeled in MATLAB® or Simulink® (requires Simulink Control Design™ software).

In order to be able to apply the extensive investigation procedures of the Control System Toolbox to a Simulink model, it must first be converted into an LTI model, which is done with the Matlab commands linmod, linmod2 or dlinmod and the Matlab command ss from the Control System Toolbox.

In addition to the possibilities shown in last lecture, Simulink can be used to quickly and easily examine a system without the Matlab commands. To do this, the so-called Linear Analysis Tool can be used.

An electric motor is an electromechanical device that converts electrical energy into mechanical torque. As a torque-producing device, the electric motor needs to have its torque (current) controlled as a priority By using the magnitude optimum. Objective of the magnitude optimum (MO) method is to maintain the closed-loop magnitude response curve as flat and as close to unity for as large bandwidth as possible for a given plant and controller structure.

The typical configuration of controllers in the motor drive systems, in which the controllers required for position, speed and current control are usually connected in a cascade.

The cascade speed control uses the current control loop designed in last lecture as a subordinate plant and is designed by using the symmetrical optimum method. The symmetrical optimum is a design method in control engineering.

Often, the speed cannot be measured due to technological circumstances or for cost reasons, but the DC machine is still to be speed-controlled. Only the actual current value is available as an output. Thus, a state observer must be designed to estimate the speed that is no longer measured.

The classical observer approach according to Luenberger uses a model identical to the plant, whereby the output error between the real output and the estimated output approximates the model behaviour to the plant behaviour via the feedback matrix L. The model is then used to estimate the speed N, which is no longer measured.

In the last lecture we calculated a luenberger observer for the dc machine with matlab and simulated the connected system with simulink. We have also found that after a step of the load torque, a considerable estimation or observer error remains. The observer cannot make this remaining estimation error zero. The following disturbance observer provides a remedy.

After we have calculated the disturbance and Luenberger observer using Control System Toolbox and verified it with simulink, we now design and programme state controllers based on this observer for the dc machine as electromechanical application.

In many practical designs, integral control is needed to counteract disturbances, plant variations, or other noises in the system. Up until now, we have not seen a state space design that has integral action. In fact state-space designs will NOT produce integral action unless we make special steps to include it! How do we introduce integral control?

The Kalman filter has revolutionized the field of control theory and has become prevalent in engineering systems. It has received a great interest from the industrial electronics community and has played a key role in many engineering fields since the 1970s, ranging from trajectory estimation, state and parameter estimation for control or diagnosis, data merging, signal processing, and so on.

Linear-quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators and servo controllers with integral action (also known as setpoint trackers). This technique allows you to trade off regulation/tracker performance and control effort, and to take into account process disturbances and measurement noise.

By the end of this lecture, students will be able to:

• Understand fundamental control concepts such as specifications, stability, and system modeling.

• Map theoretical control principles into practical MATLAB/Simulink workflows.

• See how these models translate into real-time C and C++ implementations for embedded systems.

What Students Will Learn in This Lecture:

• Trace the history of simulation techniques from analog to object-oriented methods.

• Understand why MAT-LAB and Simulink became the global standard for system simulation.

• Learn the fundamentals of Model-Based Design (MBD) and its core components.

• Differentiate between Rapid Control Prototyping (RCP) and Hardware-in-the-Loop (HIL).

• Explore how MIL, SIL, and HIL scenarios are used in modern control system development.