Classical control

Classical control

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Conventional control methods, frequently used in the industry, including PID controllers, phase lead and lag compensators, and their variations are treated in this chapter. These are the first control methods that should be applied to a new problem, and if they solve the control design specifications satisfactorily, there is no need to try more advanced control methods or alternative control architectures like two degrees-of-freedom control, for example. These classical techniques that work with Single-Input-Single-Output (SISO) transfer functions and root locus or frequency domain design methods are called conventional (or traditional) control systems here for lack of better terminology. We refrain from the use of classical control systems as techniques like state variable feedback and LQR that used to be known as modern control, and techniques like ℋ control and μ-synthesis that used to be called new approaches. These have now become classical approaches themselves as decades have passed since their introduction to the controls literature. Conventional control techniques work best for SISO, Linear-Time-Invariant (LTI) systems where the required performance specifications are given in the time-domain and/or frequency-domain. Despite the presence of a vast number of advanced control techniques in the literature, conventional control methods are widely used in the control of mechatronic systems because they can easily be implemented as real-time systems and their costs are relatively cheaper as compared to more advanced techniques. In this paper, conventional control methods such as lead, lag, lead-lag compensators, PI, PD and PID controllers are reviewed first. This is followed by analytical solution techniques for their design based on desired phase margin, gain crossover frequency, and error constant combination. The use of existing numerical optimisation based PID and controller parameter tuners in MATLAB® and Simulink® is presented next. The paper ends with the application of the multi-objective parameter space design method of Chapter 2 to PID controller design as a case study. All three of the proportional, integral and derivative gains are plotted in a three-dimensional parameter space in this case study.

Chapter Contents:

  • 3.1 Introduction to conventional control
  • 3.2 Phase lead compensation
  • 3.2.1 Characteristics of phase lead compensators
  • 3.2.2 Analytical phase lead compensator design in the frequency domain
  • 3.2.3 PD control as a special case of phase lead compensation
  • 3.3 Phase lag compensation
  • 3.3.1 Characteristics of phase lag compensators
  • 3.3.2 Analytical phase lag compensator design in the frequency domain
  • 3.3.3 PI control as a special case of phase lag control
  • 3.4 Phase lag-lead compensation
  • 3.4.1 PID control as a special case of phase lag-lead compensation
  • 3.5 Optimisation-based conventional controller design in MATLAB and Simulink
  • 3.6 Parameter space based robust conventional controller design
  • 3.6.1 Comparison of analytical approach and parameter space phase margin bound computations
  • 3.6.2 Case study of parameter space based conventional controller design
  • 3.7 Case study: Quanser QUBE™ Servo system
  • 3.8 Chapter summary and concluding remarks
  • References

Inspec keywords: three-term control; control system synthesis; compensation; state feedback; transfer functions

Other keywords: PID controllers; time domain; SISO transfer functions; phase lag compensators; root locus; single-input-single-output transfer functions; gain crossover frequency; control methods; state variable feedback; error constant combination; frequency domain; proportional-integral-derivative control; linear-time-invariant systems; phase margin; LTI systems; frequency domain design methods; control design specifications; phase lead compensators

Subjects: Control system analysis and synthesis methods

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