# Review of Advancement in Variable Valve Actuation of Internal Combustion Engines
## 10 Valve Profile Tracking of Camless VVA Systems  
In an engine without a camshaft, the accuracy and fidelity of the electronic control of valve profile are critical to achieve the desired engine performance. The valve profile tracking includes the following basic control objectives for most camless applications [81]:  
1. Valve timing control for optimum combustion phase and valve collision avoidance.
2. Valve lift control.
3. Profile area (integration of valve lift profile over time or crank angle) control for accurate air exchange.
4. Engine valve soft seating for noise control and extending durability.  
As noted by [PERSON] et al. [81], the overall valve duration control and the valve transition response (rising and falling slopes) control studied in literature can be classified into valve timing control and profile area control, respectively. For traditional cam-based engine valves, the above four properties are guaranteed by proper design of the cam profile. For camless VVAs, these control objectives can be achieved either partially or simultaneously, depending on the specific VVA system design and its application.  
Adaptive peak lift control was employed by [PERSON] et al. [93] for an EMVVA and by [PERSON] et al. [94] for an EPVVA to achieve proper valve lift repeatability.  
Feedforward control was used for valve timing control to compensate for the valve-opening or valve-closing delays for EHVVA and EPVVA by [PERSON] et al. [95] and [PERSON] et al. [38], respectively.  
Soft seating control is a challenge for the EMVVA because of nonlinear magnetic force, and it is one of the most studied subjects in the field. [PERSON] et al. [96] studied guaranteed valve response using extreme seeking control. [PERSON] and [PERSON] [97] used a combination of a feedforward linear-quadratic regulator and repetitive learning control to reduce cycle-to-cycle variations. These control designs [96; 97] were intended for single or multiple control objectives. Others dealt with the overall valve profile control as a single tracking problem. [PERSON] and [PERSON] [98], for example, applied a combination of model reference control and repetitive control to achieve asymptotic profile tracking. [PERSON] and [PERSON] [99] applied the sliding mode control to achieve repeatable tracking performance with guaranteed seating velocity. In addition, there were studies associated with the application of EMVVA systems in the combustion mode transition between SI and HCCI combustations [63], stratified lean combustion [69], and turbulent jet ignition [64].  
For an EHVVA system, [PERSON] and [PERSON] [100] and [PERSON] et al. [101] proved the effectiveness of robust repetitive control and time-varying internal-model-based control, respectively, in tracking the desired valve profile under both steady-state and transient engine operations.  
For the EHVVA system by [PERSON] et al. [84], [PERSON] et al. [81] studied the profile tracking problem without the need for complicated control scheme because of the inherent robust nature of its lift control and seating-velocity control. However, the valve timing and profile area controls are still challenging because of the nonlinear and time-varying nature of the hydraulic system, including nonlinear flow dynamics and temperature-sensitive fluid viscosity [83; 102]. A receding horizon linear-quadratic tracking (LQT) controller was designed along with a Kalman optimal state estimation, which was proven to be effective through both steady-state and transient validations.