Dynamic Surface Control For Nonlinear Systems And The Application To Servo Systems

In dynamic surface control (DSC) approach of nonlinear systems, input nonlinear partsaffect closed-loop tracking performance of output signal. Accordingly, how to improvesystem transient and steady-state performance by designing dynamic surface controlalgorithm becomes one of the issues in control society. This dissertation investigatesdynamic surface control problems of several nonlinear systems. Focused on nonlinearsystems with nonlinear input and using system structure character, extended state observer(ESO), finite-time observer and neural network observer are designed to estimate systemstates and unknown disturbance signal. Based on the observed signals, we develop outputfeedback dynamic surface controller, dynamic surface controller based on trackingdifferentiator (TD) and extended state observer, neural network dynamic surface controllerand adaptive robust dynamic surface controller. Focusing on the problems causing bynonlinear parts and disturbance in motor servo systems, dynamic surface control scheme isproposed for multi-motor driving system.The concrete works of this dissertation are dividedinto the following parts:1．The robust output precise tracking control problem of uncertain nonlinear systems inpure-feedback form with unknown input dead zone is deeply considered and investigated.By designing an extended state observer, the states immeasurable problem in traditionalfeedback control is solved, and the lumped uncertainty, which is caused by systemunknown functions and input dead zone, is estimated. In order to apply separation principle,finite-time extended state observer is designed to obtain system states and estimate thelumped uncertainty. Then, by introducing tracking differentiator, a modified dynamicsurface control approach is developed to eliminate the ‘explosion of complexity’ problemand to guarantee the tracking performance of system output. Because tracking differentiatoris a fast precise signal filter, the closed-loop control performance is significantly improvedwhen it is used in dynamic surface control instead of first-order filters. The L stability ofthe whole closed-loop system, which guarantees both the transient and steady-stateperformance, is shown by the Lyapunov method and initialization technique. Numerical examples with satisfactory results are performed to illustrate our proposed control scheme.2．Uncertain nonlinear systems with input hysteresis are studied by a noval adaptiverobust control scheme, which employs extended state observer and tracking differentiater tomodify traditional DSC method. To deal with uncertainties, ESO is used in each step ofbackstepping to online estimate and compensate unknown system functions. Based on thefinite-time convergence of ESO and combining TD, output signal precise tracking of thecontrolled nonlinear system is achieved. TD is able to precisely filter virtual stabilizingsignals and obtain their derivative signals, thus avoid the repetitive differentiating of thesame virtual control signal in the algortithm. As a result, not only the “explosion ofcomplexity” problem is solved, but also the performance of the closed-loop system isimproved. Simulation results illustrate that the proposed control algorithm is superior to theapproximator-based adaptive algorithm mentioned in references on guaranteeing systemtransient performance.3．An adaptive output feedback dynamic surface control, maintaining the prescribedperformance, for a class of uncertain nonlinear systems with multi-input and multi-output,is developed. Designing neural network observers and modifying the DSC method achieveseveral control objectives. First, to achieve output feedback control, the finite-time echostate networks (ESN) observer with fast convergence is designed to obtain the onlinesystem states. Thus the immeasurable states in traditional state feedback control areestimated and the unknown functions are approximated by ESN. Then, a modified DSCapproach is developed by introducing a high-order sliding mode differentiator (HOSM) toreplace the first-order filter in each step. Thus, the effect of filter performance onclosed-loop stability is reduced. Furthermore, the input to state stability guarantees that allsignals of the whole closed-loop system are semi-globally uniformly ultimately bounded.Specifically, the performance functions make the tracking errors converge to a compact setaround equilibrium. Two numerical examples illustrate the proposed control scheme withsatisfactory results.4．The problems of stability and tracking control for multi-motor servomechanism withunmodeled dynamics are addressed by neural active disturbance rejection control. Forrealizing output feedback, an extended state observer based on high-order sliding mode differentiator is designed to observe the unmeasured velocity. Moreover, HOSMdifferentiator is introduced to modify the traditional dynamic surface control method. Thedesigned controller solves the contradiction between rapidness and overshoot, which comesfrom the traditional proportional-integral-derivative that deals with a large number ofpractical systems with unknown disturbances. In addition, unknown functions includingfriction and disturbances are approximated by Chebyshev neural networks, in whichadaptive laws are provided by Lyapunov method. Especially, steady state and transientperformance of closed-loop system are maintained by performance function in theoreticalanalysis. Finally, experimental results are provided to illustrate our proposed approach.5．Based on ESO, this paper investigates adaptive robust DSC algorithms for motorservo systems, including servo turntable system, dual-motor driving servo system and fourmotor driving servo system. These systems have many nonlinear factors affecting controlperformance. First, backlash and friction in motor servo systems are analyzed andmathematic model of the plant are provided. Based on the obtained mathematic model ofmotor servo systems with parameter perturbance and disturbance, finite-time ESO isdesigned to estimate lumped system uncertainty. Using the online obtained disturbanceestimate signal, adaptive robust DSC is developed according to the Lyapunov stabilitytheory, maintaining the closed-loop stability and boundedness of all signals. Moreover, byparameter initialization technique, we guarantee transient performance of tracking process.Finally, effectiveness of the proposed adaptive robust DSC algorithm is validated on threedifferent test rigs.